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Technical Reports
  1. S. Gómez, A. Jüngel and I. Perugia, Structure-preserving Local Discontinuous Galerkin method for nonlinear cross-diffusion systems, arXiv:2406.17900 [math.NA].

  2. C. Lovadina, I. Perugia and M. Trezzi, A nonconforming virtual element method for advection-diffusion-reaction problems with CIP stabilization, arXiv:2407.00612 [math.NA].

  3. J. M. Melenk, I. Perugia and A. Rieder, FEM-BEM coupling for the high-frequency Helmholtz problem, arXiv:2407.04428 [math.NA].

  4. D. Pradovera, M. Nonino and I. Perugia, Geometry-based approximation of waves in complex domains, arXiv:2301.13613 [math.NA].
Book Chapters
  1. L. Mascotto, I. Perugia and A. Pichler, The nonconforming Trefftz virtual element method: general setting, applications, and dispersion analysis for the Helmholtz equation, in Antonietti, P. F., Beirão da Veiga, L., Manzini, G. (Eds.), "The Virtual Element Methods and its Applications", SEMA SIMAI Springer Series, Volume 31, 2022, Pages 363-410, Springer.

  2. R. Hiptmair, A. Moiola and I. Perugia, A Survey of Trefftz Methods for the Helmholtz Equation, in Barrenechea, G. R., Cangiani, A., Geogoulis, E. H. (Eds.), "Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations", Lecture Notes in Computational Science and Engineering (LNCSE), Volume 114, 2016, Pages 237-278, Springer.
Refereed Journal Papers
  1. A. Arnold, S. Geevers, I. Perugia and D. Ponomarev, On the limiting amplitude principle for the wave equation with variable coefficients, Comm. Part. Differ. Equat., online.

  2. S. Gómez, L. Mascotto and I. Perugia, Design and performance of a space-time virtual element method for the heat equation on prismatic meshes, Comput. Methods Appl. Mech. Engrg., 418 (2024), 116491.

  3. S. Gómez, L. Mascotto, A. Moiola and I. Perugia, Space-time virtual elements for the heat equation, SIAM J. Numer. Anal., 62 (2024), 199-228.

  4. S. Gómez, A. Moiola, I. Perugia and P. Stocker, On polynomial Trefftz spaces for the linear time-dependent Schrödinger equation, Appl. Math. Lett., 146 (2023), 108824.

  5. I. Perugia, Ch. Schwab and M. Zank, Exponential convergence of hp-time-stepping in space-time discretizations of parabolic PDEs, ESAIM: Math. Model. Numer. Anal., 57 (2023), 29-67.

  6. A. Arnold, S. Geevers, I. Perugia and D. Ponomarev, On the exponential time-decay for the one-dimensional wave equation with variable coefficients, Comm. Pure Appl. Anal., 21 (2022), 3389-3405.

  7. Ch. Erath, L. Mascotto, J. M. Melenk, I. Perugia and A. Rieder, Mortar coupling of hp-discontinuous Galerkin and boundary element methods for the Helmholtz equation, J. Sci. Comp., 92 (2022), Article number: 2.

  8. M. Braukhoff, I. Perugia and P. Stocker, An entropy structure preserving space-time formulation for cross-diffusion systems: analysis and Galerkin discretization, SIAM J. Numer. Anal., 60 (2022), 364-395.

  9. A. Arnold, S. Geevers, I. Perugia and D. Ponomarev, An adaptive finite element method for high-frequency scattering problems with smoothly varying coefficients, Comput. Math. with Appl., 109 (2022), 1-14.

  10. S. Bertoluzza, I. Perugia and D. Prada, A p-robust polygonal discontinuous Galerkin method with minus one stabilization, Math. Models Methods Appl. Sci., 31 (2021), 2695-2731.

  11. J. Gedicke, S. Geevers, I. Perugia and J. Schöberl, A polynomial-degree-robust a posteriori error estimator for Nédélec discretizations of magnetostatic problems, SIAM J. Numer. Anal., 59 (2021), 2237-2253.

  12. P. Bansal, A. Moiola, I. Perugia and Ch. Schwab, Space-time discontinuous Galerkin approximation of acoustic waves with point singularities, IMA J. Num. Anal., 41 (2021), 2056-2109.

  13. L. Mascotto, M. Melenk, I. Perugia and A. Rieder, FEM-BEM mortar coupling for the Helmholtz problem in three dimensions, Comput. Math. with Appl., 80 (2020), 2351-2378.

  14. F. Bonizzoni, M. Braukhoff, A. Jüngel and I. Perugia, A structure-preserving discontinuous Galerkin scheme for the Fisher-KPP equation, Num. Math, 146 (2020), 119-157.

  15. J. Gedicke, S. Geevers, and I. Perugia, An equilibrated a posteriori error estimator for arbitrary-order Nédélec elements for magnetostatic problems, J. Sci. Comp., 83 (2020), 58.

  16. F. Bonizzoni, F. Nobile, I. Perugia and D. Pradovera, Least-Squares Padé approximation of parametric and stochastic Helmholtz maps, Adv. Comput. Math., 46 (2020), 46.

  17. I. Perugia, J. Schöberl, P. Stocker, and Ch. Wintersteiger, Tent pitching and Trefftz-DG method for the acoustic wave equation, Comput. Math. with Appl., 70 (2020), 2987-3000.

  18. F. Bonizzoni, F. Nobile, I. Perugia and D. Pradovera, Fast Least-Squares Padé approximation of problems with normal operators and meromorphic structure, Math. Comp., 89 (2020), 1229-1257.

  19. L. Mascotto, I. Perugia and A. Pichler, A nonconforming Trefftz virtual element method for the Helmholtz problem, Math. Models Methods Appl. Sci., 29 (2019), 1619-1656.

  20. S. Congreve, J. Gedicke and I. Perugia, Robust adaptive hp discontinuous Galerkin finite element methods for the Helmholtz equation, SIAM J. Sci.Comp., 41 (2019), A1121–A1147.

  21. L. Mascotto, I. Perugia and A. Pichler, A nonconforming Trefftz virtual element method for the Helmholtz problem: numerical aspects, Comp. Meth. Appl. Mech. Engrg., 347 (2019), 445-476.

  22. S. Congreve, P. Houston and I. Perugia, Adaptive refinement for hp-version Trefftz discontinuous Galerkin methods for the homogeneous Helmholtz problem, Adv. Comput. Math., 45 (2019), 361-393.

  23. L. Mascotto, I. Perugia and A. Pichler, Non-conforming harmonic virtual element method: h- and p-versions, J. Sci. Comp., 77 (2018), 1874-1908.

  24. F. Bonizzoni, F. Nobile and I. Perugia, Convergence analysis of Padé approximations for Helmholtz frequency response problems, ESAIM: Math. Model. Numer. Anal., 52 (2018), 1261-1284.

  25. A. Moiola and I. Perugia, A space–time Trefftz discontinuous Galerkin method for the acoustic wave equation in first-order formulation, Num. Math., 139 (2018), 389-435.

  26. S. Esterhazy, F. M. Schneider, I. Perugia and G. Bokelmann, Application of high-order FEM to the P-wave propagation around and inside an underground cavity, Geophysics, 82 (2017), T197-T206.

  27. F. M. Schneider, S. Esterhazy, I. Perugia and G. Bokelmann, Seismic resonances of spherical acoustic cavities, Geophys. Prospect., doi:10.1111/1365-2478.12523.

  28. I. Perugia, P. Pietra and A. Russo, A Plane Wave Virtual Element Method for the Helmholtz Problem, ESAIM: Math. Model. Numer. Anal., 50 (2016), 783-808.

  29. F. Kretzschmar, A. Moiola, I. Perugia and S. M. Schnepp, A priori error analysis of space-time Trefftz discontinuous Galerkin methods for wave problems, IMA J. Numer. Anal., 36 (2016), 1599-1635.

  30. R. Hiptmair, A. Moiola and I. Perugia, Plane Wave Discontinuous Galerkin Methods: Exponential Convergence of the hp-version, Found. Comp. Math., 16 (2016), 637-675.

  31. R. Hiptmair, A. Moiola, I. Perugia and Ch. Schwab, Approximation by harmonic polynomials in star-shaped domains and exponential convergence of Trefftz hp-DGFEM, ESAIM: Math. Model. Numer. Anal., 48 (2014), 727-752.

  32. R. Hiptmair, A. Moiola and I. Perugia, Trefftz discontinuous Galerkin methods for acoustic scattering on locally refined meshes, Appl. Numer. Math., 79 (2014), 79-91.

  33. R. Hiptmair, A. Moiola and I. Perugia, Error analysis of Trefftz-discontinuous Galerkin methods for the time-harmonic Maxwell equations, Math. Comp., 82 (2013), 247-268.

  34. F. Cavalli, G. Naldi and I. Perugia, Discontinuous Galerkin approximation of relaxation models for linear and nonlinear diffusion equations, SIAM J. Sci. Comp., 34 (2012), A105-A136.

  35. R. Hiptmair, A. Moiola and I. Perugia, Stability results for the time-harmonic Maxwell equations with impedance boundary conditions, Math. Mod. Meth. Appl. Sci., 21 (2011), 2263-2287.

  36. A. Moiola, R. Hiptmair and I. Perugia, Plane wave approximation of homogeneous Helmholtz solutions, Z. Angew. Math. Phys., 62 (2011), 809-837.

  37. A. Moiola, R. Hiptmair and I. Perugia, Vekua theory for the Helmholtz operator, Z. Angew. Math. Phys., 62 (2011), 779-807.

  38. R. Hiptmair, A. Moiola and I. Perugia, Plane wave discontinuous Galerkin methods for the 2D Helmholtz equation: analysis of the p-version, SIAM J. Numer. Anal., 49 (2011), 264-284.

  39. A. Buffa, I. Perugia and T. Warburton, The mortar-discontinuous Galerkin method for the 2D Maxwell eigenproblem, J. Sci. Comp., 40 (2009), 86-114.

  40. C. J. Gittelson, R. Hiptmair and I. Perugia, Plane wave discontinuous Galerkin methods: Analysis of the h-version, M2AN Math. Model. Numer. Anal., 43 (2009), 297-331.

  41. A. Buffa, P. Houston and I. Perugia, Discontinuous Galerkin Computation of the Maxwell Eigenvalues on Simplicial Meshes, J. Comput. Appl. Math., 204 (2007), 317-333.

  42. P. Houston, I. Perugia and D. Schötzau, An a posteriori error indicator for discontinuous Galerkin discretizations of H(curl)-elliptic partial differential equations, IMA J. Numer. Anal., 27 (2007), 122-150.

  43. A. Buffa and I. Perugia, Discontinuous Galerkin approximation of the Maxwell eigenproblem, SIAM J. Numer. Anal., 44 (2006), 2198-2226.

  44. P. F. Antonietti, A. Buffa and I. Perugia, Discontinuous Galerkin approximation of the Laplace eigenproblem, Comput. Methods Appl. Mech. Engrg., 195 (2006), 3483-3503.

  45. P. Houston, I. Perugia, A. Schneebeli and D. Schötzau, Mixed discontinuous Galerkin approximation of the Maxwell operator: the indefinite case, M2AN Math. Model. Numer. Anal., 39 (2005), 727-753.

  46. P. Houston, I. Perugia, A. Schneebeli and D. Schötzau, Interior penalty method for the indefinite time-harmonic Maxwell equations, Numer. Math., 100 (2005), 485-518.

  47. P. Hansbo, C. Lovadina, I. Perugia and G. Sangalli, A Lagrange multiplier method for the finite element solution of elliptic interface problems using non-matching meshes, Numer. Math., 100 (2005), 91-115.

  48. P. Houston, I. Perugia and D. Schötzau, Energy norm a posteriori error estimation for mixed discontinuous Galerkin approximations of the Maxwell operator, Comput. Methods Appl. Mech. Engrg., 194 (2005), 499-510.

  49. P. Houston, I. Perugia and D. Schötzau, Mixed discontinuous Galerkin approximation of the Maxwell operator: non-stabilized formulation, J. Sci. Comp., 22-23 (2005), 315-346.

  50. P. Alotto and I. Perugia, Matrix Properties of a Vector Potential Cell Method for Magnetostatics, IEEE Trans. on Magnetics, 40 (2004), 1045-1048.

  51. P. Houston, I. Perugia and D. Schötzau, Nonconforming mixed finite element approximations to time-harmonic eddy current problems, IEEE Trans. on Magnetics, 40 (2004), 1268-1273.

  52. P. Houston, I. Perugia and D. Schötzau, Mixed discontinuous Galerkin approximation of the Maxwell operator, SIAM J. Numer. Anal., 42 (2004), 434-459.

  53. I. Perugia and D. Schötzau, The hp-local discontinuous Galerkin method for low-frequency time-harmonic Maxwell equations, Math. Comp., 72 (2003), 1179-1214.

  54. I. Perugia, D. Schötzau and P. Monk, Stabilized interior penalty methods for the time-harmonic Maxwell equations, Comp. Meth. Appl. Mech. Engrg., 191 (2002), 4675-4697.

  55. P. Alotto, A. Bertoni, I. Perugia and D. Schötzau, Efficient use of the Local Discontinuous Galerkin method for meshes sliding on a circular boundary, IEEE Trans. on Magnetics, 38 (2002), 405-408.

  56. I. Perugia and D. Schötzau, An hp-analysis of the local discontinuous Galerkin method for diffusion problems, J. Sci. Comp., 17 (2002), 561-571.

  57. P. Castillo, B. Cockburn, I. Perugia and D. Schötzau, Local discontinuous Galerkin method for elliptic problems, Commun. Numer. Meth. Engrg., 18 (2002), 69-75.

  58. I. Perugia and D. Schötzau, On the coupling of local discontinuous Galerkin and conforming finite element methods, J. Sci. Comp., 16 (2001), 411-433.

  59. B. Cockburn, G. Kanschat, I. Perugia and D. Schötzau, Superconvergence of the local discontinuous Galerkin method for elliptic problems on Cartesian grids, SIAM J. Numer. Anal., 39 (2001), 264-285.

  60. P. Alotto, A. Bertoni, I. Perugia and D. Schötzau, Discontinuous finite element methods for the simulation of rotating electrical machines, COMPEL, 20 (2001), 448-462.

  61. P. Fernandes and I. Perugia, Vector potential formulation for magnetostatics and modeling of permanent magnets, IMA J. Appl. Math., 66 (2001), 293-318.

  62. P. Castillo, B. Cockburn, I. Perugia and D. Schötzau, An a priori error analysis of the Local Discontinuous Galerkin method for elliptic problems, SIAM J. Numer. Anal., 38 (2000), 1676-1706.

  63. I. Perugia and V. Simoncini, Block-diagonal and indefinite symmetric preconditioners for mixed finite element formulations, Numer. Linear Algebra Appl., 7 (2000), 585-616.

  64. P. Alotto and I. Perugia, Tree-cotree implicit condensation in Magnetostatics, IEEE Trans. on Magnetics, 36 (2000), 1523-1526.

  65. P. Alotto and I. Perugia, A field-based finite element method for magnetostatics derived from an error minimisation approach, Internat. J. Numer. Methods Engrg., 49 (2000), 573-598.

  66. P. Alotto and I. Perugia, An adaptive mixed formulation for 3D magnetostatics, COMPEL, 19 (2000), 106-120.

  67. P. Alotto and I. Perugia, Mixed finite element methods and tree-cotree implicit condensation, Calcolo, 36 (1999), 233-248.

  68. I. Perugia, A mixed formulation for 3D magnetostatic problems: theoretical analysis and face-edge finite element approximation, Numer. Math., 84 (1999), 305-326.

  69. I. Perugia, V. Simoncini and M. Arioli, Linear algebra methods in a mixed approximation of magnetostatic problems, SIAM J. Sci. Comput., 21 (1999), 1085-1101.

  70. D. Boffi, P. Fernandes, L. Gastaldi and I. Perugia, Computational models of electromagnetic resonators: analysis of edge element approximation, SIAM J. Numer. Anal., 36 (1999), 1264-1290.

  71. P. Alotto, F. Delfino, P. Molfino, M. Nervi and I. Perugia, A mixed face-edge finite element formulation for 3D magnetostatic problems, IEEE Trans. on Magnetics, 34 (1998), 2445-2448.

  72. P. Di Barba, A. Savini and I. Perugia, Mixed finite elements for the simulation of fields and forces in electromagnetic devices, IEEE Trans. on Magnetics, 34 (1998), 3572-3575.

  73. P. Di Barba, I. Perugia and A. Savini, Recent Experiences on Mixed Finite Elements for 2D Simulation of Magnetic Fields, COMPEL, 17 (1998), 674-681.

  74. I. Perugia, A field-based mixed formulation for the 2-D magnetostatic problem, SIAM J. Numer. Anal., 34 (1997), 2382-2391.

  75. I. Perugia and T. Scapolla, Optimal rectangular MITC finite elements for Reissner-Mindlin plates, Numer. Methods Partial Differential Equations, 13 (1997), 575-585.

  76. F. Brezzi, P. Di Barba, L.D. Marini, I. Perugia and A. Savini, A Novel Field-Based Mixed Formulation of Magnetostatics, IEEE Trans. on Magnetics, 32 (1996), 635-638.

  77. I. Perugia, A class of quadrilateral finite elements for the Stokes problem, Appl. Math. Lett., 6 (1993), 27-30.
Other Papers
  1. I. Perugia, Peter Monk's contributions to Numerical Analysis and Maxwell's equations, Comput. Math. Appl., 74 (2017), 2645-2649.

  2. P. Houston, I. Perugia and D. Schötzau, Recent developments in Discontinuous Galerkin methods for the time-harmonic Maxwell equations, International Compumag Society Newsletter, 11 (2004), 11-17.

  3. C. Lovadina and I. Perugia, Finite element methods for piezoelectric Reissner-Mindlin plates, Rend. Ist. Lomb. Sez. A - Analisi Numerica, 129 (1995), 121-134.
Refereed Conference Proceedings
  1. S. Congreve, J. Gedicke and I. Perugia, Numerical investigation of the conditioning for plane wave discontinuous Galerkin methods, Radu, F.A., Kumar, K., Berre, I., Nordbotten, J.M., Pop, I.S. (Eds.), Numerical Mathematics and Advanced Applications ENUMATH 2017: Proceedings of ENUMATH 2017, the 12th European Conference on Numerical Mathematics and Advanced Applications, Voss, Norway, September 25-29, 2017, LNCSE, Vol. 126, Springer, 2019.

  2. F. Kretzschmar, A. Moiola, I. Perugia and S. M. Schnepp, The space-time Trefftz discontinuous Galerkin method for the wave equation, Proceedings of Waves 2015 - The 12th International Conference on Mathematical and Numerical Aspects of Waves, Karlsruhe, Germany, July 20-24, 2015, pp. 140-141.

  3. P. F. Antonietti, I. Perugia and D. Zaliani, Schwarz domain decomposition preconditioners for plane wave discontinuous Galerkin methods, Abdulle, A., Deparis, S., Kressner, D., Nobile, F., Picasso, M. (Eds.), Numerical Mathematics and Advanced Applications-ENUMATH 2013: Proceedings of ENUMATH 2013, the 10th European Conference on Numerical Mathematics and Advanced Applications, Lausanne, August 2013, LNCSE, Vol. 103. Springer, 2014, pp. 557-572.

  4. R. Hiptmair, A. Moiola, I. Perugia and Ch. Schwab, Trefftz-discontinuous Galerkin methods: hp-version and exponential convergence, Proceedings of Waves 2013 - The 11th International Conference on Mathematical and Numerical Aspects of Waves, Gammarth, Tunisia, June 3-7, 2013, pp. 359-360.

  5. G. Naldi, F. Cavalli and I. Perugia, Discontinuous Galerkin approximation of porous Fisher-Kolmogorov equations, Proceeding of SIMAI 2012, June 25, 2012-28, 2012, Torino, Italy, Comm. Appl. Ind. Math., 4 (2013).

  6. R. Hiptmair and I. Perugia, Mixed plane wave discontinuous Galerkin methods, in Domain Decomposition Methods in Science and Engineering XVIII, M. Bercovier, M.J. Gander, R. Kornhuber and O. Widlund, eds., Lecture Notes in Computational Science and Engineering, Spinger, 2008, pp. 51-62.

  7. A. Buffa and I. Perugia, Discontinuous Galerkin approximation of eigenvalue problems, Proceeding of the Third M.I.T. Conference on Computational Fluid and Solid Mechanics, June 14-17, 2005, Cambridge MA, USA (Elsevier).

  8. P. Houston, I. Perugia A. Scheneebeli and D. Schötzau, Discontinuous Galerkin methods for the time-harmonic Maxwell equations, Proceedings of ENUMATH 2003 the European Conference on Numerical Mathematics and Advanced Applications, August 18-22, 2003, Prague, Czech Republic, (Springer), pp. 483-492.

  9. I. Perugia, D. Schötzau and J. Warsa On a discontinuous Galerkin method for radiation-diffusion problems, Proceedings of ENUMATH 2003 the European Conference on Numerical Mathematics and Advanced Applications, August 18-22, 2003, Prague, Czech Republic (Springer), pp. 687-697.

  10. P. Houston, I. Perugia and D. Schötzau, Nonconforming mixed finite element approximations to time-harmonic eddy current problems, Proceedings of XIV COMPUMAG Conference on Computation of Electromagnetic Fields, July 13-17, 2003, Saratoga Springs NY, USA.

  11. P. Alotto, I. Perugia, Matrix properties of a vector potential cell method for magnetostatics, Proceedings of XIV COMPUMAG Conference on Computation of Electromagnetic Fields, July 13-17, 2003, Saratoga Springs NY, USA.

  12. C. Lovadina, R. Nascimbene, I. Perugia and P. Venini, Mixed methods for interface problems, Proceeding of the Second M.I.T. Conference on Computational Fluid and Solid Mechanics, June 17-20, 2003, Cambridge MA, USA (Elsevier), pp. 2053-2056.

  13. P. Houston, I. Perugia and D. Schötzau, hp-DGFEM for Maxwell's equations, Proceedings of ENUMATH 2001 the European Conference on Numerical Mathematics and Advanced Applications, July 23-28, 2001, Ischia Porto, Italy (Springer), pp. 785-794.

  14. P. Alotto, A. Bertoni, I. Perugia and D. Schötzau, Efficient use of the Local Discontinuous Galerkin method for meshes sliding on a circular boundary, Proceedings of XIII COMPUMAG Conference on Computation of Electromagnetic Fields, July 2-5, 2001, Evian, France.

  15. P. Alotto, A. Bertoni, I. Perugia and D. Schötzau, Discontinuous Finite Element Methods for the Simulation of Rotating Electrical Machines, IX International IGTE Symposium on Numerical Field Calculation in Electrical Engineering, September 11-14, 2000, Graz, Austria.

  16. P. Alotto and I. Perugia, Tree-cotree implicit condensation in magnetostatics, Proceedings of XII COMPUMAG Conference on Computation of Electromagnetic Fields, October 25-28, 1999, Sapporo, Japan.

  17. P. Alotto and I. Perugia, An adaptive mixed formulation and code for 3D magnetostatics, VIII International IGTE Symposium on Numerical Field Calculation in Electrical Engineering, September 21-24, 1998, Graz, Austria.

  18. P. Alotto, F. Delfino, P. Molfino, M. Nervi and I. Perugia, A mixed face-edge finite element formulation for 3D magnetostatic problem, Proceedings of the XI COMPUMAG Conference on Computation of Electromagnetic Fields, November 2-6, 1997, Rio de Janeiro, Brasil.

  19. P. Di Barba, A. Savini and I. Perugia, Mixed finite elements for the simulation of fields and forces in electromagnetic devices, Proceedings of the XI COMPUMAG Conference on Computation of Electromagnetic Fields, November 2-6, 1997, Rio de Janeiro, Brasil.

  20. P. Di Barba, I. Perugia and A. Savini, Recent Experiences on Mixed Finite Elements for 2D Simulation of Magnetic Fields, Proceedings of the IX ISTET International Symposium on Theoretical Electrical Engineering, June 9-11, 1997, Palermo, Italy.

  21. D. Boffi, P. Fernandes, L. Gastaldi and I. Perugia, Edge approximation of eigenvalue problems arising from electromagnetics, Proceedings of the Second ECCOMAS Conference on Numerical Methods in Engineering, September 9-13, 1996, Paris, France (John Wiley & Sons).

  22. F. Brezzi, P. Di Barba, L.D. Marini, I. Perugia and A. Savini, A Novel Field-Based Mixed Formulation of Magnetostatics, Proceedings of the X COMPUMAG Conf. on Computation of Electromagnetic Fields, July 10-13, 1995, Berlin, Germany.

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