Staff profile

I am an Associate Professor in High-Performance Computing within the Department of Engineeringat Durham University, specialising in Finite Element Methods (FEMs) that I applied to a varietyof linear and non-linear problems in solid mechanics, fluid dynamics, photonics, acoustics andradiative heat transfer. My research interests include discontinuous Galerkin methods, error estimators, adaptivity, multi-level methods, preconditioners and fracture.

I am also an expert in Deep Neural Networks (DNNs) to tackle a variety of problems such as AI-based machine monitoring systems, natural language processing and artificial language processing.

• Finite Element Methods (FEMs) and Artificial Intelligence (AI).

Chapter in book

• The Good, the Bad, and the Ugly
  
  Dallabona, A., & Giani, S. (in press). The Good, the Bad, and the Ugly. In A. Sikarskie (Ed.), Storytelling in Luxury Fashion: Brands, Visual Cultures, and Technologies. Routledge.
• Review of Discontinuous Galerkin Finite Element Methods for Partial Differential Equations on Complicated Domains
  
  Antonietti, P., Cangiani, A., Collis, J., Dong, Z., Georgoulis, E., Giani, S., & Houston, P. (2016). Review of Discontinuous Galerkin Finite Element Methods for Partial Differential Equations on Complicated Domains. In G. Barrenechea, F. Brezzi, A. Cangiani, & E. Georgoulis (Eds.), Building bridges : connections and challenges in modern approaches to numerical partial differential equations. (pp. 279-308). Springer Verlag. https://doi.org/10.1007/978-3-319-41640-3_9
• Chapter Chapter 28
  
  Giani, S., & Houston, P. (2010). Chapter Chapter 28. In ADIGMA - A European Initiative on the Development of Adaptive Higher-Order Variational Methods for Aerospace Applications. https://doi.org/10.1007/978-3-642-03707-8_28

Conference Paper

• Modelling Fracture Behaviour in Fibre-Hybrid 3D Woven Composites
  
  Weatherburn, A., Reinarz, A., Giani, S., & Szyniszewski, S. (2024). Modelling Fracture Behaviour in Fibre-Hybrid 3D Woven Composites. In W. M. Coombs (Ed.), UKACM Proceedings 2024 (pp. 162-166). UK Association for Computational Mechanics. https://doi.org/10.62512/conf.ukacm2024.002
• Immersed traction boundary conditions in phase field fracture modelling
  
  Sims, B., Bird, R. E., Coombs, W. M., & Giani, S. (2024). Immersed traction boundary conditions in phase field fracture modelling. In W. M. Coombs (Ed.), UKACM Proceedings 2024 (pp. 201-204). UK Association for Computational Mechanics. https://doi.org/10.62512/conf.ukacm2024.045
• Recursive autoencoder network for prediction of CAD model parameters from STEP files
  
  Miles, V., Giani, S., Vogt, O., & Kafieh, R. (2024). Recursive autoencoder network for prediction of CAD model parameters from STEP files. Procedia Computer Science, 232, 3239-3246. https://doi.org/10.1016/j.procs.2024.02.139
• An investigation into the methods for modelling pre-existing cracks in phase field problems
  
  Sims, B., Bird, R., Giani, S., & Coombs, W. (2023). An investigation into the methods for modelling pre-existing cracks in phase field problems. Presented at UKACM 2023, Warwick, UK.
• Classification of Pulmonary Hypertension by Shape Analysis of the Human Right Ventricle: Robustness and Preliminary Association with Clinical Outcomes
  
  Desmond, E. L., Xu, J., Wong, T. C., Simon, M. S., Giani, S., & Brigham, J. C. (2019). Classification of Pulmonary Hypertension by Shape Analysis of the Human Right Ventricle: Robustness and Preliminary Association with Clinical Outcomes. In Computational and Mathematical Biomedical Engineering 2019 Proceedings (pp. 643-646). CMBE.
• Level set based topology optimisation using high-order reinitialisation methods and the discontinuous Galerkin method
  
  Adams, T., Giani, S., & Coombs, W. (2017). Level set based topology optimisation using high-order reinitialisation methods and the discontinuous Galerkin method. In A. Faramarzi & S. Dirar (Eds.), Proceedings of the 25th Conference on Computational Mechanics (UKACM 2017) : 11th – 13th April 2017, School of Engineering, University of Birmingham, Birmingham, UK. (pp. 18-21). University of Birmingham.
• A discontinuous Galerkin hp-adaptive finite element method for brittlecrack propagation
  
  Bird, R., Coombs, W., & Giani, S. (2017). A discontinuous Galerkin hp-adaptive finite element method for brittlecrack propagation. In A. Faramarzi & S. Dirar (Eds.), Proceedings of the 25th Conference on Computational Mechanics (UKACM 2017): 11th – 13th April 2017, School of Engineering, University of Birmingham, Birmingham, UK. (pp. 138-141). University of Birmingham.
• Topology optimisation using level set methods and the discontinuous Galerkin method
  
  Adams, T., Giani, S., & Coombs, W. (2016). Topology optimisation using level set methods and the discontinuous Galerkin method. In Proceedings of the 24th UK Conference of the Association for Computational Mechanics in Engineering, 31 March - 01 April 2016, Cardiff University, Cardiff. (pp. 6-9). Cardiff University.
• Two dimensional configurational-force-driven crack propagation using the discontinuous Galerkin method with rp-adaptivity
  
  Bird, R., Coombs, W., & Giani, S. (2016). Two dimensional configurational-force-driven crack propagation using the discontinuous Galerkin method with rp-adaptivity. In Proceedings of the 24th UK Conference of the Association for Computational Mechanics in Engineering, 31 March - 01 April 2016, Cardiff University, Cardiff. (pp. 137-140). Cardiff University.

Conference Proceeding

• UKACM Proceedings 2024
  
  Coombs, W. M. (Ed.). (2024). UKACM Proceedings 2024. UK Association for Computational Mechanics and Durham University. https://doi.org/10.62512/conf.ukacm2024

Journal Article

• Enhancing lecture capture with deep learning
  
  Sales, R. M., & Giani, S. (2024). Enhancing lecture capture with deep learning. Advances in Engineering Software, 196, Article 103732. https://doi.org/10.1016/j.advengsoft.2024.103732
• An hp-adaptive discontinuous Galerkin method for phase field fracture
  
  Bird, R. E., Augarde, C. E., Coombs, W. M., Duddu, R., Giani, S., Huynh, P. T., & Sims, B. (2023). An hp-adaptive discontinuous Galerkin method for phase field fracture. Computer Methods in Applied Mechanics and Engineering, 416, Article 116336. https://doi.org/10.1016/j.cma.2023.116336
• Convolutional neural network framework for wind turbine electromechanical fault detection
  
  Stone, E., Giani, S., Zappalá, D., & Crabtree, C. (2023). Convolutional neural network framework for wind turbine electromechanical fault detection. Wind Energy, 26(10), 1082-1097. https://doi.org/10.1002/we.2857
• khp-adaptive spectral projection based discontinuous Galerkin method for the numerical solution of wave equations with memory
  
  Giani, S., Engström, C., & Grubišić, L. (2023). khp-adaptive spectral projection based discontinuous Galerkin method for the numerical solution of wave equations with memory. Journal of Computational and Applied Mathematics, 429, Article 115212. https://doi.org/10.1016/j.cam.2023.115212
• Approaching STEP file analysis as a language processing task: A robust and scale-invariant solution for machining feature recognition
  
  Miles, V., Giani, S., & Vogt, O. (2023). Approaching STEP file analysis as a language processing task: A robust and scale-invariant solution for machining feature recognition. Journal of Computational and Applied Mathematics, 427, Article 115166. https://doi.org/10.1016/j.cam.2023.115166
• Numerical solution of distributed-order time-fractional diffusion-wave equations using Laplace transforms
  
  Engström, C., Giani, S., & Grubišić, L. (2023). Numerical solution of distributed-order time-fractional diffusion-wave equations using Laplace transforms. Journal of Computational and Applied Mathematics, 425, Article 115035. https://doi.org/10.1016/j.cam.2022.115035
• Recursive Encoder Network for the Automatic Analysis of STEP Files
  
  Miles, V., Giani, S., & Vogt, O. (2023). Recursive Encoder Network for the Automatic Analysis of STEP Files. Journal of Intelligent Manufacturing, 34(1), 181-196. https://doi.org/10.1007/s10845-022-01998-x
• On Effects of Concentrated Loads on Perforated Sensitive Shells of Revolution
  
  Giani, S., & Hakula, H. (2023). On Effects of Concentrated Loads on Perforated Sensitive Shells of Revolution. Journal of Computational and Applied Mathematics, 428, Article 115165. https://doi.org/10.1016/j.cam.2023.115165
• Camera-Based System for the Automatic Detection of Vehicle Axle Count and Speed Using Convolutional Neural Networks
  
  Miles, V., Gurr, F., & Giani, S. (2022). Camera-Based System for the Automatic Detection of Vehicle Axle Count and Speed Using Convolutional Neural Networks. International Journal of Intelligent Transportation Systems Research, 20(3), 778-792. https://doi.org/10.1007/s13177-022-00325-1
• A spectral projection based method for the numerical solution of wave equations with memory
  
  Engström, C., Giani, S., & Grubišić, L. (2022). A spectral projection based method for the numerical solution of wave equations with memory. Applied Mathematics Letters, 127, Article 107844. https://doi.org/10.1016/j.aml.2021.107844
• Adaptive Configurational Force-based crack propagation for brittle and fatigue analysis
  
  Bird, R., Coombs, W., & Giani, S. (2022). Adaptive Configurational Force-based crack propagation for brittle and fatigue analysis. International Journal for Numerical Methods in Engineering, 123(7), 1673-1709. https://doi.org/10.1002/nme.6911
• Higher Order Composite DG approximations of Gross–Pitaevskii ground state: benchmark results and experiments
  
  Engström, C., Giani, S., & Grubišić, L. (2022). Higher Order Composite DG approximations of Gross–Pitaevskii ground state: benchmark results and experiments. Journal of Computational and Applied Mathematics, 400, Article 113652. https://doi.org/10.1016/j.cam.2021.113652
• Free Vibration of Perforated Cylindrical Shells of Revolution: Asymptotics and Effective Material Parameters
  
  Giani, S., & Hakula, H. (2022). Free Vibration of Perforated Cylindrical Shells of Revolution: Asymptotics and Effective Material Parameters. Computer Methods in Applied Mechanics and Engineering, 403(A), Article 115700. https://doi.org/10.1016/j.cma.2022.115700
• An open source hp-adaptive discontinuous Galerkin finite element solver for linear elasticity
  
  Wiltshire, T., Bird, R. E., Coombs, W. M., & Giani, S. (2022). An open source hp-adaptive discontinuous Galerkin finite element solver for linear elasticity. Advances in Engineering Software, 171. https://doi.org/10.1016/j.advengsoft.2022.103147
• Using Company-Specific Headlines and Convolutional Neural Networks to Predict Stock Fluctuations
  
  Readshaw, J., & Giani, S. (2021). Using Company-Specific Headlines and Convolutional Neural Networks to Predict Stock Fluctuations. Neural Computing and Applications, 33(24), 17353-17367. https://doi.org/10.1007/s00521-021-06324-9
• On Effects of Perforated Domains on Parameter-Dependent Free Vibration
  
  Giani, S., & Hakula, H. (2021). On Effects of Perforated Domains on Parameter-Dependent Free Vibration. Journal of Computational and Applied Mathematics, 394, Article 113526. https://doi.org/10.1016/j.cam.2021.113526
• Solving Elliptic Eigenproblems with Adaptive Multimesh hp-FEM
  
  Giani, S., & Solin, P. (2021). Solving Elliptic Eigenproblems with Adaptive Multimesh hp-FEM. Journal of Computational and Applied Mathematics, 394, Article 113528. https://doi.org/10.1016/j.cam.2021.113528
• A Posteriori Error Estimates for Elliptic Eigenvalue Problems Using Auxiliary Subspace Techniques
  
  Giani, S., Grubišic, L., Hakula, H., & Ovall, J. S. (2021). A Posteriori Error Estimates for Elliptic Eigenvalue Problems Using Auxiliary Subspace Techniques. Journal of Scientific Computing, 88(3), Article 55. https://doi.org/10.1007/s10915-021-01572-2
• Quasi-optimal mesh sequence construction through Smoothed Adaptive Finite Element Methods
  
  Mulita, O., Giani, S., & Heltai, L. (2021). Quasi-optimal mesh sequence construction through Smoothed Adaptive Finite Element Methods. SIAM Journal on Scientific Computing, 43(3), A2211-A2241. https://doi.org/10.1137/19m1262097
• Smoothed-adaptive perturbed inverse iteration for elliptic eigenvalue problems
  
  Giani, S., Grubišić, L., Heltai, L., & Mulita, O. (2021). Smoothed-adaptive perturbed inverse iteration for elliptic eigenvalue problems. Computational Methods in Applied Mathematics, 21(2), 385-405. https://doi.org/10.1515/cmam-2020-0027
• On Effective Material Parameters of Thin Perforated Shells under Static Loading
  
  Giani, S., & Hakula, H. (2020). On Effective Material Parameters of Thin Perforated Shells under Static Loading. Computer Methods in Applied Mechanics and Engineering, 367, Article 113094. https://doi.org/10.1016/j.cma.2020.113094
• Multi-hp adaptive discontinuous Galerkin methods for simplified PN approximations of 3D radiative transfer in non-gray media
  
  Giani, S., & Seaid, M. (2020). Multi-hp adaptive discontinuous Galerkin methods for simplified PN approximations of 3D radiative transfer in non-gray media. Applied Numerical Mathematics, 150, 252-273. https://doi.org/10.1016/j.apnum.2019.09.018
• An adaptive composite discontinuous Galerkin method for elliptic problems on complicated domains with discontinuous coefficients
  
  Giani, S. (2020). An adaptive composite discontinuous Galerkin method for elliptic problems on complicated domains with discontinuous coefficients. Advances in Computational Mathematics, 46(1), Article 13. https://doi.org/10.1007/s10444-020-09759-1
• A parabolic level set reinitialisation method using a discontinuous Galerkin discretisation
  
  Adams, T., McLeish, N., Giani, S., & Coombs, W. (2019). A parabolic level set reinitialisation method using a discontinuous Galerkin discretisation. Computers and Mathematics With Applications, 78(9), 2944-2960. https://doi.org/10.1016/j.camwa.2019.01.032
• hp-adaptive discontinuous Galerkin methods for non-stationary convection-diffusion problems
  
  Cangiani, A., Georgoulis, E., Giani, S., & Metcalfe, S. (2019). hp-adaptive discontinuous Galerkin methods for non-stationary convection-diffusion problems. Computers and Mathematics With Applications, 78(9), 3090-3104. https://doi.org/10.1016/j.camwa.2019.04.002
• Accurate Configuration Force Evaluation via hp-adaptive Discontinuous Galerkin Finite Element Analysis
  
  Bird, R., Coombs, W., & Giani, S. (2019). Accurate Configuration Force Evaluation via hp-adaptive Discontinuous Galerkin Finite Element Analysis. Engineering Fracture Mechanics, 216, Article 106370. https://doi.org/10.1016/j.engfracmech.2019.02.029
• A posteriori discontinuous Galerkin error estimator for linear elasticity
  
  Bird, R., Coombs, W., & Giani, S. (2019). A posteriori discontinuous Galerkin error estimator for linear elasticity. Applied Mathematics and Computation, 344-345, 78-96. https://doi.org/10.1016/j.amc.2018.08.039
• A high-order elliptic PDE based level set reinitialisation method using a discontinuous Galerkin discretisation
  
  Adams, T., Giani, S., & Coombs, W. (2019). A high-order elliptic PDE based level set reinitialisation method using a discontinuous Galerkin discretisation. Journal of Computational Physics, 379, 373-391. https://doi.org/10.1016/j.jcp.2018.12.003
• Rapid non-linear finite element analysis of continuous and discontinuous Galerkin methods in MATLAB
  
  O’Sullivan, S., Bird, R., Coombs, W., & Giani, S. (2019). Rapid non-linear finite element analysis of continuous and discontinuous Galerkin methods in MATLAB. Computers and Mathematics With Applications, 78(9), 3007-3026. https://doi.org/10.1016/j.camwa.2019.03.012
• hp-adaptive celatus enriched discontinuous Galerkin method for second-order elliptic source problems
  
  Giani, S. (2018). hp-adaptive celatus enriched discontinuous Galerkin method for second-order elliptic source problems. SIAM Journal on Scientific Computing, 40(5), B1391-B1418. https://doi.org/10.1137/17m1149912
• Reliable anisotropic-adaptive discontinuous Galerkin method for simplified P_N approximations of radiative transfer
  
  Giani, S. (2018). Reliable anisotropic-adaptive discontinuous Galerkin method for simplified P_N approximations of radiative transfer. Journal of Computational and Applied Mathematics, 337, 225-243. https://doi.org/10.1016/j.cam.2017.12.039
• A quasi-static discontinuous Galerkin configurational force crack propagation method for brittle materials
  
  Bird, R., Coombs, W., & Giani, S. (2018). A quasi-static discontinuous Galerkin configurational force crack propagation method for brittle materials. International Journal for Numerical Methods in Engineering, 113(7), 1061-1080. https://doi.org/10.1002/nme.5699
• Earthquake Nucleation Size: Evidence of Loading Rate Dependence in Laboratory Faults
  
  Guérin‐Marthe, S., Nielsen, S., Bird, R., Giani, S., & Di Toro, G. (2018). Earthquake Nucleation Size: Evidence of Loading Rate Dependence in Laboratory Faults. Journal of Geophysical Research. Solid Earth, 124(1), 689-708. https://doi.org/10.1029/2018jb016803
• Fast native-MATLAB stiffness assembly for SIPG linear elasticity
  
  Bird, R., Coombs, W., & Giani, S. (2017). Fast native-MATLAB stiffness assembly for SIPG linear elasticity. Computers and Mathematics With Applications, 74(12), 3209-3230. https://doi.org/10.1016/j.camwa.2017.08.022
• An a posteriori estimator of eigenvalue/eigenvector error for penalty-type discontinuous Galerkin methods
  
  Giani, S., Grubišić, L., Hakula, H., & Ovall, J. (2017). An a posteriori estimator of eigenvalue/eigenvector error for penalty-type discontinuous Galerkin methods. Applied Mathematics and Computation, 319, 562-574. https://doi.org/10.1016/j.amc.2017.07.007
• Efficient and reliable hp-FEM estimates for quadratic eigenvalue problems and photonic crystal applications
  
  Engström, C., Giani, S., & Grubišić, L. (2016). Efficient and reliable hp-FEM estimates for quadratic eigenvalue problems and photonic crystal applications. Computers and Mathematics With Applications, 72(4), 952-973. https://doi.org/10.1016/j.camwa.2016.06.001
• Robust error estimates for approximations of non-self-adjoint eigenvalue problems
  
  Giani, S., Grubišić, L., Międlar, A., & Ovall, J. (2016). Robust error estimates for approximations of non-self-adjoint eigenvalue problems. Numerische Mathematik, 133(3), 471-495. https://doi.org/10.1007/s00211-015-0752-3
• Benchmark results for testing adaptive finite element eigenvalue procedures part 2 (conforming eigenvector and eigenvalue estimates)
  
  Giani, S., Grubišić, L., & Ovall, J. (2016). Benchmark results for testing adaptive finite element eigenvalue procedures part 2 (conforming eigenvector and eigenvalue estimates). Applied Numerical Mathematics, 102, 1-16. https://doi.org/10.1016/j.apnum.2015.12.001
• hp-adaptive discontinuous Galerkin methods for simplified PN approximations of frequency-dependent radiative transfer
  
  Giani, S., & Seaid, M. (2016). hp-adaptive discontinuous Galerkin methods for simplified PN approximations of frequency-dependent radiative transfer. Computer Methods in Applied Mechanics and Engineering, 301, 52-79. https://doi.org/10.1016/j.cma.2015.12.013
• Solving elliptic eigenvalue problems on polygonal meshes using discontinuous Galerkin composite finite element methods
  
  Giani, S. (2015). Solving elliptic eigenvalue problems on polygonal meshes using discontinuous Galerkin composite finite element methods. Applied Mathematics and Computation, 267, 618-631. https://doi.org/10.1016/j.amc.2015.01.011
• hp-Adaptive composite discontinuous Galerkin methods for elliptic eigenvalue problems on complicated domains
  
  Giani, S. (2015). hp-Adaptive composite discontinuous Galerkin methods for elliptic eigenvalue problems on complicated domains. Applied Mathematics and Computation, 267, 604-617. https://doi.org/10.1016/j.amc.2015.01.031
• Goal-oriented adaptive composite discontinuous Galerkin methods for incompressible flows
  
  Giani, S., & Houston, P. (2014). Goal-oriented adaptive composite discontinuous Galerkin methods for incompressible flows. Journal of Computational and Applied Mathematics, 270, 32-42. https://doi.org/10.1016/j.cam.2014.03.007
• A hp-adaptive discontinuous Galerkin method for plasmonic waveguides
  
  Giani, S. (2014). A hp-adaptive discontinuous Galerkin method for plasmonic waveguides. Journal of Computational and Applied Mathematics, 270, 12-20. https://doi.org/10.1016/j.cam.2014.03.009
• hp–Adaptive composite discontinuous Galerkin methods for elliptic problems on complicated domains
  
  Giani, S., & Houston, P. (2014). hp–Adaptive composite discontinuous Galerkin methods for elliptic problems on complicated domains. Numerical Methods for Partial Differential Equations, 30(4), 1342-1367. https://doi.org/10.1002/num.21872
• Domain Decomposition Preconditioners for Discontinuous Galerkin Methods for Elliptic Problems on Complicated Domains
  
  Antonietti, P., Giani, S., & Houston, P. (2014). Domain Decomposition Preconditioners for Discontinuous Galerkin Methods for Elliptic Problems on Complicated Domains. Journal of Scientific Computing, 60(1), 203-227. https://doi.org/10.1007/s10915-013-9792-y
• An a-posteriori error estimate for hp-adaptive DG methods for convection–diffusion problems on anisotropically refined meshes
  
  Giani, S., Schötzau, D., & Zhu, L. (2014). An a-posteriori error estimate for hp-adaptive DG methods for convection–diffusion problems on anisotropically refined meshes. Computers and Mathematics With Applications, 67(4), 869-887. https://doi.org/10.1016/j.camwa.2012.10.015
• An a posteriori error estimator for hp-adaptive continuous Galerkin methods for photonic crystal applications
  
  Giani, S. (2013). An a posteriori error estimator for hp-adaptive continuous Galerkin methods for photonic crystal applications. Computing, 95(5), 395-414. https://doi.org/10.1007/s00607-012-0244-6
• hp-Version Composite Discontinuous Galerkin Methods for Elliptic Problems on Complicated Domains
  
  Antonietti, P., Giani, S., & Houston, P. (2013). hp-Version Composite Discontinuous Galerkin Methods for Elliptic Problems on Complicated Domains. SIAM Journal on Scientific Computing, 35(3), A1417-A1439. https://doi.org/10.1137/120877246
• An iterative adaptive hp-FEM method for non-symmetric elliptic eigenvalue problems
  
  Solin, P., & Giani, S. (2013). An iterative adaptive hp-FEM method for non-symmetric elliptic eigenvalue problems. Computing, 95(1 Supplement), S183-S213. https://doi.org/10.1007/s00607-012-0251-7
• Error control for hp -adaptive approximations of semi-definite eigenvalue problems
  
  Giani, S., Grubišić, L., & Ovall, J. (2013). Error control for hp -adaptive approximations of semi-definite eigenvalue problems. Computing, 95(1), 235-257. https://doi.org/10.1007/s00607-012-0260-6
• High-order/hp-adaptive discontinuous Galerkin finite element methods for acoustic problems
  
  Giani, S. (2013). High-order/hp-adaptive discontinuous Galerkin finite element methods for acoustic problems. Computing, 95(1 Supplement), S215-S234. https://doi.org/10.1007/s00607-012-0253-5
• An a-posteriori error estimate for hp-adaptive DG methods for elliptic eigenvalue problems on anisotropically refined meshes
  
  Giani, S., & Hall, E. (2013). An a-posteriori error estimate for hp-adaptive DG methods for elliptic eigenvalue problems on anisotropically refined meshes. Computing, 95(1 Supplement), S319-S341. https://doi.org/10.1007/s00607-012-0261-5
• An a posteriori error estimator for hp-adaptive discontinuous Galerkin methods for computing band gaps in photonic crystals
  
  Giani, S. (2012). An a posteriori error estimator for hp-adaptive discontinuous Galerkin methods for computing band gaps in photonic crystals. Journal of Computational and Applied Mathematics, 236(18), 4810-4826. https://doi.org/10.1016/j.cam.2012.02.007
• An Iterative Adaptive Finite Element Method for Elliptic Eigenvalue Problems.
  
  Solin, P., & Giani, S. (2012). An Iterative Adaptive Finite Element Method for Elliptic Eigenvalue Problems. Journal of Computational and Applied Mathematics, 236(18), 4582-4599. https://doi.org/10.1016/j.cam.2012.05.002
• An A Posteriori Error Estimator for Hp-Adaptive Discontinuous Galerkin Methods for Elliptic Eigenvalue Problems
  
  Giani, S., & Hall, E. (2012). An A Posteriori Error Estimator for Hp-Adaptive Discontinuous Galerkin Methods for Elliptic Eigenvalue Problems. Mathematical Models and Methods in Applied Sciences, 22(10). https://doi.org/10.1142/s0218202512500303
• Convergent adaptive finite element methods for photonic crystal applications
  
  Giani, S. (2012). Convergent adaptive finite element methods for photonic crystal applications. Mathematical Models and Methods in Applied Sciences, 22(10). https://doi.org/10.1142/s0218202512500285
• Boundary element dynamical energy analysis: a versatile method for solving two or three dimensional wave problems in the high frequency limit
  
  Chappell, D., Tanner, G., & Giani, S. (2012). Boundary element dynamical energy analysis: a versatile method for solving two or three dimensional wave problems in the high frequency limit. Journal of Computational Physics, 231(18), 6181-6191. https://doi.org/10.1016/j.jcp.2012.05.028
• Adaptive finite element methods for computing band gaps in photonic crystals
  
  Giani, S., & Graham, I. (2012). Adaptive finite element methods for computing band gaps in photonic crystals. Numerische Mathematik, 121(1), 31-64. https://doi.org/10.1007/s00211-011-0425-9
• Benchmark results for testing adaptive finite element eigenvalue procedures
  
  Giani, S., Grubisic, L., & Ovall, J. (2012). Benchmark results for testing adaptive finite element eigenvalue procedures. Applied Numerical Mathematics, 62(2), 121-140. https://doi.org/10.1016/j.apnum.2011.10.007
• Anisotropic hp-adaptive discontinuous Galerkin finite element methods for compressible fluid flows
  
  Giani, S., & Houston, P. (2012). Anisotropic hp-adaptive discontinuous Galerkin finite element methods for compressible fluid flows. International Journal of Numerical Analysis and Modeling, 9(4), 928-949.
• Dynamical energy analysis for built-up acoustic systems at high frequencies
  
  Chappell, D., Giani, S., & Tanner, G. (2011). Dynamical energy analysis for built-up acoustic systems at high frequencies. The Journal of the Acoustical Society of America, 130(3), 1420-1429. https://doi.org/10.1121/1.3621041
• Energy Norm A-Posteriori Error Estimation for hp-Adaptive Discontinuous Galerkin Methods for Elliptic Problems in Three Dimensions
  
  Zhu, L., Giani, S., Houston, P., & Schötzau, D. (2011). Energy Norm A-Posteriori Error Estimation for hp-Adaptive Discontinuous Galerkin Methods for Elliptic Problems in Three Dimensions. Mathematical Models and Methods in Applied Sciences, 21(02), 267-306. https://doi.org/10.1142/s0218202511005052
• A convergent adaptive method for elliptic eigenvalue problems
  
  Giani, S., & Graham, I. (2009). A convergent adaptive method for elliptic eigenvalue problems. SIAM Journal on Numerical Analysis, 47(2), 1067-1091. https://doi.org/10.1137/070697264