Gómez, Sergio; Moiola, Andrea; Perugia, Ilaria; Stocker, Paul On polynomial Trefftz spaces for the linear time-dependent Schrödinger equation. (English) Zbl 07741242 Appl. Math. Lett. 146, Article ID 108824, 10 p. (2023). MSC: 65Mxx 78Mxx 41Axx PDFBibTeX XMLCite \textit{S. Gómez} et al., Appl. Math. Lett. 146, Article ID 108824, 10 p. (2023; Zbl 07741242) Full Text: DOI arXiv
Erath, Christoph; Mascotto, Lorenzo; Melenk, Jens M.; Perugia, Ilaria; Rieder, Alexander Mortar coupling of \(hp\)-discontinuous Galerkin and boundary element methods for the Helmholtz equation. (English) Zbl 1492.65304 J. Sci. Comput. 92, No. 1, Paper No. 2, 41 p. (2022). MSC: 65N30 65N38 65N50 35J05 76Q05 76M10 76M15 35Q35 PDFBibTeX XMLCite \textit{C. Erath} et al., J. Sci. Comput. 92, No. 1, Paper No. 2, 41 p. (2022; Zbl 1492.65304) Full Text: DOI arXiv
Bansal, Pratyuksh; Moiola, Andrea; Perugia, Ilaria; Schwab, Christoph Space-time discontinuous Galerkin approximation of acoustic waves with point singularities. (English) Zbl 07528299 IMA J. Numer. Anal. 41, No. 3, 2056-2109 (2021). MSC: 65Mxx PDFBibTeX XMLCite \textit{P. Bansal} et al., IMA J. Numer. Anal. 41, No. 3, 2056--2109 (2021; Zbl 07528299) Full Text: DOI arXiv
Bertoluzza, Silvia; Perugia, Ilaria; Prada, Daniele A \(p\)-robust polygonal discontinuous Galerkin method with minus one stabilization. (English) Zbl 1501.65107 Math. Models Methods Appl. Sci. 31, No. 13, 2695-2731 (2021). Reviewer: Bülent Karasözen (Ankara) MSC: 65N30 65N12 65N15 35J05 PDFBibTeX XMLCite \textit{S. Bertoluzza} et al., Math. Models Methods Appl. Sci. 31, No. 13, 2695--2731 (2021; Zbl 1501.65107) Full Text: DOI arXiv
Bonizzoni, Francesca; Braukhoff, Marcel; Jüngel, Ansgar; Perugia, Ilaria A structure-preserving discontinuous Galerkin scheme for the Fisher-KPP equation. (English) Zbl 1452.65225 Numer. Math. 146, No. 1, 119-157 (2020). MSC: 65M60 65M06 65M12 35K20 35K57 35B09 35D35 92D25 35Q92 PDFBibTeX XMLCite \textit{F. Bonizzoni} et al., Numer. Math. 146, No. 1, 119--157 (2020; Zbl 1452.65225) Full Text: DOI arXiv
Perugia, Ilaria; Schöberl, Joachim; Stocker, Paul; Wintersteiger, Christoph Tent pitching and Trefftz-DG method for the acoustic wave equation. (English) Zbl 1447.65087 Comput. Math. Appl. 79, No. 10, 2987-3000 (2020). Reviewer: Marius Ghergu (Dublin) MSC: 65M60 65M12 65M15 65N50 65Y05 41A25 35L05 PDFBibTeX XMLCite \textit{I. Perugia} et al., Comput. Math. Appl. 79, No. 10, 2987--3000 (2020; Zbl 1447.65087) Full Text: DOI arXiv
Congreve, Scott; Houston, Paul; Perugia, Ilaria Adaptive refinement for \(hp\)-version Trefftz discontinuous Galerkin methods for the homogeneous Helmholtz problem. (English) Zbl 1419.65105 Adv. Comput. Math. 45, No. 1, 361-393 (2019). Reviewer: Abdallah Bradji (Annaba) MSC: 65N30 65N50 35J05 78M10 PDFBibTeX XMLCite \textit{S. Congreve} et al., Adv. Comput. Math. 45, No. 1, 361--393 (2019; Zbl 1419.65105) Full Text: DOI arXiv
Congreve, Scott; Gedicke, Joscha; Perugia, Ilaria Robust adaptive \(hp\) discontinuous Galerkin finite element methods for the Helmholtz equation. (English) Zbl 1414.65029 SIAM J. Sci. Comput. 41, No. 2, A1121-A1147 (2019). MSC: 65N15 65N30 65N50 35J05 PDFBibTeX XMLCite \textit{S. Congreve} et al., SIAM J. Sci. Comput. 41, No. 2, A1121--A1147 (2019; Zbl 1414.65029) Full Text: DOI arXiv
Moiola, Andrea; Perugia, Ilaria A space-time Trefftz discontinuous Galerkin method for the acoustic wave equation in first-order formulation. (English) Zbl 1421.65026 Numer. Math. 138, No. 2, 389-435 (2018). Reviewer: Konstantinos Chrysafinos (Athens) MSC: 65M60 65M15 41A10 41A25 35L05 PDFBibTeX XMLCite \textit{A. Moiola} and \textit{I. Perugia}, Numer. Math. 138, No. 2, 389--435 (2018; Zbl 1421.65026) Full Text: DOI arXiv
Kretzschmar, Fritz; Moiola, Andrea; Perugia, Ilaria; Schnepp, Sascha M. A priori error analysis of space-time Trefftz discontinuous Galerkin methods for wave problems. (English) Zbl 1433.65240 IMA J. Numer. Anal. 36, No. 4, 1599-1635 (2016). MSC: 65M70 65M15 35Q61 PDFBibTeX XMLCite \textit{F. Kretzschmar} et al., IMA J. Numer. Anal. 36, No. 4, 1599--1635 (2016; Zbl 1433.65240) Full Text: DOI arXiv
Hiptmair, Ralf; Moiola, Andrea; Perugia, Ilaria A survey of Trefftz methods for the Helmholtz equation. (English) Zbl 1357.65282 Barrenechea, Gabriel R. (ed.) et al., Building bridges: connections and challenges in modern approaches to numerical partial differential equations. Selected papers based on the presentations at the 101st LMS-EPSRC symposium, Durham, UK, July 8–16, 2014. Cham: Springer (ISBN 978-3-319-41638-0/hbk; 978-3-319-41640-3/ebook). Lecture Notes in Computational Science and Engineering 114, 237-279 (2016); erratum ibid. 114, E1 (2016). MSC: 65N38 35J05 65N30 65N80 PDFBibTeX XMLCite \textit{R. Hiptmair} et al., Lect. Notes Comput. Sci. Eng. 114, 237--279 (2016; Zbl 1357.65282) Full Text: DOI Link
Hiptmair, R.; Moiola, A.; Perugia, I. Plane wave discontinuous Galerkin methods: exponential convergence of the \(hp\)-version. (English) Zbl 1347.65176 Found. Comput. Math. 16, No. 3, 637-675 (2016). Reviewer: Ivan Secrieru (Chişinău) MSC: 65N30 65N50 35J05 65N12 PDFBibTeX XMLCite \textit{R. Hiptmair} et al., Found. Comput. Math. 16, No. 3, 637--675 (2016; Zbl 1347.65176) Full Text: DOI
Hiptmair, Ralf; Moiola, Andrea; Perugia, Ilaria Trefftz discontinuous Galerkin methods for acoustic scattering on locally refined meshes. (English) Zbl 1288.65166 Appl. Numer. Math. 79, 79-91 (2014). MSC: 65N30 35J05 76Q05 65N12 65N15 76M10 PDFBibTeX XMLCite \textit{R. Hiptmair} et al., Appl. Numer. Math. 79, 79--91 (2014; Zbl 1288.65166) Full Text: DOI Link
Naldi, Giovanni; Cavalli, Fausto; Perugia, Ilaria Discontinuous Galerkin approximation of porous Fisher-Kolmogorov equations. (English) Zbl 1329.65227 Commun. Appl. Ind. Math. 4, Article ID 446, 18 p. (2013). MSC: 65M60 35K20 35K57 PDFBibTeX XMLCite \textit{G. Naldi} et al., Commun. Appl. Ind. Math. 4, Article ID 446, 18 p. (2013; Zbl 1329.65227)
Hiptmair, Ralf; Moiola, Andrea; Perugia, Ilaria Error analysis of Trefftz-discontinuous Galerkin methods for the time-harmonic Maxwell equations. (English) Zbl 1269.78013 Math. Comput. 82, No. 281, 247-268 (2013). Reviewer: Marius Ghergu (Dublin) MSC: 78M10 78M30 PDFBibTeX XMLCite \textit{R. Hiptmair} et al., Math. Comput. 82, No. 281, 247--268 (2013; Zbl 1269.78013) Full Text: DOI arXiv
Cavalli, Fausto; Naldi, Giovanni; Perugia, Ilaria Discontinuous Galerkin approximation of relaxation models for linear and nonlinear diffusion equations. (English) Zbl 1273.65137 SIAM J. Sci. Comput. 34, No. 1, A105-A136 (2012). MSC: 65M60 65M12 35K55 35K65 PDFBibTeX XMLCite \textit{F. Cavalli} et al., SIAM J. Sci. Comput. 34, No. 1, A105--A136 (2012; Zbl 1273.65137) Full Text: DOI Link
Hiptmair, R.; Moiola, A.; Perugia, I. Plane wave discontinuous Galerkin methods for the 2D Helmholtz equation: analysis of the \(p\)-version. (English) Zbl 1229.65215 SIAM J. Numer. Anal. 49, No. 1, 264-284 (2011). Reviewer: Marius Ghergu (Dublin) MSC: 65N30 65N12 35J05 65N15 PDFBibTeX XMLCite \textit{R. Hiptmair} et al., SIAM J. Numer. Anal. 49, No. 1, 264--284 (2011; Zbl 1229.65215) Full Text: DOI
Buffa, Annalisa; Perugia, Ilaria; Warburton, Tim The mortar-discontinuous Galerkin method for the 2D Maxwell eigenproblem. (English) Zbl 1203.65246 J. Sci. Comput. 40, No. 1-3, 86-114 (2009). MSC: 65N30 65N25 78M10 PDFBibTeX XMLCite \textit{A. Buffa} et al., J. Sci. Comput. 40, No. 1--3, 86--114 (2009; Zbl 1203.65246) Full Text: DOI
Gittelson, Claude J.; Hiptmair, Ralf; Perugia, Ilaria Plane wave discontinuous Galerkin methods: Analysis of the \(h\)-version. (English) Zbl 1165.65076 ESAIM, Math. Model. Numer. Anal. 43, No. 2, 297-331 (2009). Reviewer: Seenith Sivasundaram (Daytona Beach) MSC: 65N30 65N15 35J05 65N12 PDFBibTeX XMLCite \textit{C. J. Gittelson} et al., ESAIM, Math. Model. Numer. Anal. 43, No. 2, 297--331 (2009; Zbl 1165.65076) Full Text: DOI EuDML Link
Buffa, Annalisa; Houston, Paul; Perugia, Ilaria Discontinuous Galerkin computation of the Maxwell eigenvalues on simplicial meshes. (English) Zbl 1131.78007 J. Comput. Appl. Math. 204, No. 2, 317-333 (2007). Reviewer: Francisco José Pena Brage (Santiago de Compostela) MSC: 78M10 65N30 PDFBibTeX XMLCite \textit{A. Buffa} et al., J. Comput. Appl. Math. 204, No. 2, 317--333 (2007; Zbl 1131.78007) Full Text: DOI
Houston, Paul; Perugia, Ilaria; Schötzau, Dominik An a posteriori error indicator for discontinuous Galerkin discretizations of \(H\)(curl)-elliptic partial differential equations. (English) Zbl 1148.65088 IMA J. Numer. Anal. 27, No. 1, 122-150 (2007). MSC: 65N30 78M10 PDFBibTeX XMLCite \textit{P. Houston} et al., IMA J. Numer. Anal. 27, No. 1, 122--150 (2007; Zbl 1148.65088) Full Text: DOI
Buffa, Annalisa; Perugia, Ilaria Discontinuous Galerkin approximation of heterogeneous Maxwell source problem. (English) Zbl 1242.78028 Bol. Soc. Esp. Mat. Apl., S\(\vec{\text{e}}\)MA 34, 33-44 (2006). MSC: 78M10 65N30 PDFBibTeX XMLCite \textit{A. Buffa} and \textit{I. Perugia}, Bol. Soc. Esp. Mat. Apl., S\(\vec{\text{e}}\)MA 34, 33--44 (2006; Zbl 1242.78028)
Buffa, Annalisa; Perugia, Ilaria Discontinuous Galerkin approximation of the Maxwell eigenproblem. (English) Zbl 1344.65110 SIAM J. Numer. Anal. 44, No. 5, 2198-2226 (2006). MSC: 65N30 65N25 PDFBibTeX XMLCite \textit{A. Buffa} and \textit{I. Perugia}, SIAM J. Numer. Anal. 44, No. 5, 2198--2226 (2006; Zbl 1344.65110) Full Text: DOI
Antonietti, Paola F.; Buffa, Annalisa; Perugia, Ilaria Discontinuous Galerkin approximation of the Laplace eigenproblem. (English) Zbl 1168.65410 Comput. Methods Appl. Mech. Eng. 195, No. 25-28, 3483-3503 (2006). MSC: 65N25 65N30 35P15 65N12 PDFBibTeX XMLCite \textit{P. F. Antonietti} et al., Comput. Methods Appl. Mech. Eng. 195, No. 25--28, 3483--3503 (2006; Zbl 1168.65410) Full Text: DOI
Houston, Paul; Perugia, Ilaria; Schneebeli, Anna; Schötzau, Dominik Mixed discontinuous Galerkin approximation of the Maxwell operator: the indefinite case. (English) Zbl 1087.65106 ESAIM, Math. Model. Numer. Anal. 39, No. 4, 727-753 (2005). Reviewer: Johannes Elschner (Berlin) MSC: 65N30 78M10 35Q60 78A25 65N15 PDFBibTeX XMLCite \textit{P. Houston} et al., ESAIM, Math. Model. Numer. Anal. 39, No. 4, 727--753 (2005; Zbl 1087.65106) Full Text: DOI Numdam EuDML
Houston, Paul; Perugia, Ilaria; Schneebeli, Anna; Schötzau, Dominik Interior penalty method for the indefinite time-harmonic Maxwell equations. (English) Zbl 1071.65155 Numer. Math. 100, No. 3, 485-518 (2005). Reviewer: Răzvan Răducanu (Iaşi) MSC: 65N30 35Q60 78A25 78M10 PDFBibTeX XMLCite \textit{P. Houston} et al., Numer. Math. 100, No. 3, 485--518 (2005; Zbl 1071.65155) Full Text: DOI
Houston, Paul; Perugia, Ilaria; Schötzau, Dominik Mixed discontinuous Galerkin approximation of the Maxwell operator: non-stabilized formulation. (English) Zbl 1091.78017 J. Sci. Comput. 22-23, 315-346 (2005). Reviewer: Teodora-Liliana Rădulescu (Craiova) MSC: 78M10 65Z05 PDFBibTeX XMLCite \textit{P. Houston} et al., J. Sci. Comput. 22--23, 315--346 (2005; Zbl 1091.78017) Full Text: DOI
Houston, Paul; Perugia, Ilaria; Schötzau, Dominik Energy norm a posteriori error estimation for mixed discontinuous Galerkin approximations of the Maxwell operator. (English) Zbl 1063.78021 Comput. Methods Appl. Mech. Eng. 194, No. 2-5, 499-510 (2005). MSC: 78M10 65N15 65N30 PDFBibTeX XMLCite \textit{P. Houston} et al., Comput. Methods Appl. Mech. Eng. 194, No. 2--5, 499--510 (2005; Zbl 1063.78021) Full Text: DOI
Houston, Paul; Perugia, Ilaria; Schötzau, Dominik Mixed discontinuous Galerkin approximation of the Maxwell operator. (English) Zbl 1084.65115 SIAM J. Numer. Anal. 42, No. 1, 434-459 (2004). Reviewer: Fumio Kikuchi (Tokyo) MSC: 65N30 35Q40 65N12 78A25 78M10 PDFBibTeX XMLCite \textit{P. Houston} et al., SIAM J. Numer. Anal. 42, No. 1, 434--459 (2004; Zbl 1084.65115) Full Text: DOI
Perugia, Ilaria; Schötzau, Dominik; Warsa, James On a discontinuous Galerkin method for radiation-diffusion problems. (English) Zbl 1057.65086 Feistauer, M. (ed.) et al., Numerical mathematics and advanced applications. Proceedings of ENUMATH 2003, the 5th European conference on numerical mathematics and advanced applications, Prague, Czech Republic, August 18–22, 2003. Berlin: Springer (ISBN 3-540-21460-7/hbk). 687-697 (2004). MSC: 65N30 65N15 35J25 82C70 PDFBibTeX XMLCite \textit{I. Perugia} et al., in: Numerical mathematics and advanced applications. Proceedings of ENUMATH 2003, the 5th European conference on numerical mathematics and advanced applications, Prague, Czech Republic, August 18--22, 2003. Berlin: Springer. 687--697 (2004; Zbl 1057.65086)
Houston, Paul; Perugia, Ilaria; Schneebeli, Anna; Schötzau, Dominik Discontinuous Galerkin methods for the time-harmonic Maxwell equations. (English) Zbl 1170.78305 Feistauer, M. (ed.) et al., Numerical mathematics and advanced applications. Proceedings of ENUMATH 2003, the 5th European conference on numerical mathematics and advanced applications, Prague, Czech Republic, August 18–22, 2003. Berlin: Springer (ISBN 3-540-21460-7/hbk). 483-492 (2004). Reviewer: Xavier Antoine (Vandœuvre-lès-Nancy) MSC: 78-06 PDFBibTeX XMLCite \textit{P. Houston} et al., in: Numerical mathematics and advanced applications. Proceedings of ENUMATH 2003, the 5th European conference on numerical mathematics and advanced applications, Prague, Czech Republic, August 18--22, 2003. Berlin: Springer. 483--492 (2004; Zbl 1170.78305)
Perugia, I.; Schötzau, D.; Monk, P. Stabilized interior penalty methods for the time-harmonic Maxwell equations. (English) Zbl 1040.78011 Comput. Methods Appl. Mech. Eng. 191, No. 41-42, 4675-4697 (2002). MSC: 78M10 65N30 PDFBibTeX XMLCite \textit{I. Perugia} et al., Comput. Methods Appl. Mech. Eng. 191, No. 41--42, 4675--4697 (2002; Zbl 1040.78011) Full Text: DOI
Perugia, Ilaria; Schötzau, Dominik An \(hp\)-analysis of the local discontinuous Galerkin method for diffusion problems. (English) Zbl 1001.76060 J. Sci. Comput. 17, No. 1-4, 561-571 (2002). MSC: 76M10 76R50 PDFBibTeX XMLCite \textit{I. Perugia} and \textit{D. Schötzau}, J. Sci. Comput. 17, No. 1--4, 561--571 (2002; Zbl 1001.76060) Full Text: DOI
Castillo, P.; Cockburn, B.; Perugia, I.; Schötzau, D. Local discontinuous Galerkin methods for elliptic problems. (English) Zbl 0994.65121 Commun. Numer. Methods Eng. 18, No. 1, 69-75 (2002). MSC: 65N30 65N15 35J05 PDFBibTeX XMLCite \textit{P. Castillo} et al., Commun. Numer. Methods Eng. 18, No. 1, 69--75 (2002; Zbl 0994.65121) Full Text: DOI
Perugia, Ilaria; Schötzau, Dominik On the coupling of local discontinuous Galerkin and conforming finite element methods. (English) Zbl 0995.65117 J. Sci. Comput. 16, No. 4, 411-433 (2001). Reviewer: Ziwen Jiang (Shandong) MSC: 65N30 65N15 35J05 35J25 PDFBibTeX XMLCite \textit{I. Perugia} and \textit{D. Schötzau}, J. Sci. Comput. 16, No. 4, 411--433 (2001; Zbl 0995.65117) Full Text: DOI
Cockburn, Bernardo; Kanschat, Guido; Perugia, Ilaria; Schötzau, Dominik Superconvergence of the local discontinuous Galerkin method for elliptic problems on Cartesian grids. (English) Zbl 1041.65080 SIAM J. Numer. Anal. 39, No. 1, 264-285 (2001). MSC: 65N12 65N30 35J25 PDFBibTeX XMLCite \textit{B. Cockburn} et al., SIAM J. Numer. Anal. 39, No. 1, 264--285 (2001; Zbl 1041.65080) Full Text: DOI
Castillo, Paul; Cockburn, Bernardo; Perugia, Ilaria; Schötzau, Dominik An a priori error analysis of the local discontinuous Galerkin method for elliptic problems. (English) Zbl 0987.65111 SIAM J. Numer. Anal. 38, No. 5, 1676-1706 (2000). Reviewer: H.Marcinkowska (Wrocław) MSC: 65N15 65N30 35J25 65N12 PDFBibTeX XMLCite \textit{P. Castillo} et al., SIAM J. Numer. Anal. 38, No. 5, 1676--1706 (2000; Zbl 0987.65111) Full Text: DOI