Discontinuous Galerkin Methods for Acoustic Wave Propagation in Polygons

citation_journal_title=Math. Comput.; citation_title=Graded mesh approximation in weighted Sobolev spaces and elliptic equations in 2D; citation_author=J Adler, V Nistor; citation_volume=84; citation_issue=295; citation_publication_date=2015; citation_pages=2191-2220; citation_doi=10.1090/S0025-5718-2015-02934-2; citation_id=CR1 citation_journal_title=SIAM J. Numer. Anal.; citation_title=Unified analysis of discontinuous Galerkin methods for elliptic problems; citation_author=D Arnold, F Brezzi, B Cockburn, D Marini; citation_volume=39; citation_issue=5; citation_publication_date=2002; citation_pages=1749-1779; citation_doi=10.1137/S0036142901384162; citation_id=CR2 citation_journal_title=SIAM J. Numer. Anal.; citation_title=The - version of the finite element method for domains with curved boundaries; citation_author=I Babuška, BQ Guo; citation_volume=25; citation_issue=4; citation_publication_date=1988; citation_pages=837-861; citation_doi=10.1137/0725048; citation_id=CR3 citation_journal_title=SIAM J. Math. Anal.; citation_title=Regularity of the solution of elliptic problems with piecewise analytic data. I. Boundary value problems for linear elliptic equation of second order; citation_author=I Babuška, BQ Guo; citation_volume=19; citation_issue=1; citation_publication_date=1988; citation_pages=172-203; citation_doi=10.1137/0519014; citation_id=CR4 citation_journal_title=Numer. Math.; citation_title=Direct and inverse error estimates for finite elements with mesh refinements; citation_author=I Babuška, RB Kellogg, J Pitkäranta; citation_volume=33; citation_issue=4; citation_publication_date=1979; citation_pages=447-471; citation_doi=10.1007/BF01399326; citation_id=CR5 citation_journal_title=Numer. Math.; citation_title=Improving the rate of convergence of ‘high order finite elements’ on polygons and domains with cusps; citation_author=C Băcuţă, V Nistor, LT Zikatanov; citation_volume=100; citation_issue=2; citation_publication_date=2005; citation_pages=165-184; citation_doi=10.1007/s00211-005-0588-3; citation_id=CR6 citation_journal_title=Rev. Roum. Math. Pures Appl.; citation_title=Differential operators on domains with conical points: precise uniform regularity estimates; citation_author=C Băcuţă, H Li, V Nistor; citation_volume=62; citation_issue=3; citation_publication_date=2017; citation_pages=383-411; citation_id=CR7 Cohen, G., Joly, P., Tordjman, N.: Construction and analysis of higher order finite elements with mass lumping for the wave equation. In: Second International Conference on Mathematical and Numerical Aspects of Wave Propagation (Newark, DE, 1993), SIAM, Philadelphia, PA, pp. 152–160 (1993) Dautray, R., Lions, J.-L.: Mathematical analysis and numerical methods for science and technology, vol. 5, Springer, Berlin. Evolution problems. I, With the collaboration of Michel Artola, Michel Cessenat and Hélène Lanchon, Translated from the French by Alan Craig (1992) citation_title=Theory and Practice of Finite Elements, Applied Mathematical Sciences; citation_publication_date=2004; citation_id=CR10; citation_author=A Ern; citation_author=J-L Guermond; citation_publisher=Springer citation_journal_title=IMA J. Numer. Anal.; citation_title=Convergence rates for adaptive finite elements; citation_author=FD Gaspoz, P Morin; citation_volume=29; citation_issue=4; citation_publication_date=2009; citation_pages=917-936; citation_doi=10.1093/imanum/drn039; citation_id=CR11 citation_title=Elliptic Problems in Nonsmooth Domains, Monographs and Studies in Mathematics; citation_publication_date=1985; citation_id=CR12; citation_author=P Grisvard; citation_publisher=Pitman citation_journal_title=SIAM J. Numer. Anal.; citation_title=Discontinuous Galerkin finite element method for the wave equation; citation_author=M Grote, A Schneebeli, D Schötzau; citation_volume=44; citation_issue=6; citation_publication_date=2006; citation_pages=2408-2431; citation_doi=10.1137/05063194X; citation_id=CR13 citation_journal_title=J. Sci. Comput.; citation_title=Optimal error estimates for the fully discrete interior penalty DG method for the wave equation; citation_author=M Grote, D Schötzau; citation_volume=40; citation_publication_date=2009; citation_pages=257-272; citation_doi=10.1007/s10915-008-9247-z; citation_id=CR14 citation_journal_title=Comput. Mech.; citation_title=The -version of the finite element method. Part I: the basic approximation results; citation_author=BQ Guo, I Babuška; citation_volume=1; citation_publication_date=1986; citation_pages=21-41; citation_doi=10.1007/BF00298636; citation_id=CR15 citation_journal_title=SIAM J. Numer. Anal.; citation_title=Error analysis of a second-order locally implicit method for linear Maxwell’s equations; citation_author=M Hochbruck, A Sturm; citation_volume=54; citation_issue=5; citation_publication_date=2016; citation_pages=3167-3191; citation_doi=10.1137/15M1038037; citation_id=CR16 Jones, E., Oliphant, T., Peterson, P., et al.: SciPy: Open Source Scientific Tools for Python (2001). https://www.scipy.org . Accessed 05 Apr 2018 citation_journal_title=J. Sci. Comput.; citation_title=Variational space–time methods for the wave equation; citation_author=U Köcher, M Bause; citation_volume=61; citation_issue=2; citation_publication_date=2014; citation_pages=424-453; citation_doi=10.1007/s10915-014-9831-3; citation_id=CR18 citation_journal_title=Algebra i Analiz; citation_title=On the asymptotic behavior of solutions of the Neumann problem for hyperbolic systems in domains with conical points; citation_author=AY Kokotov, BA Plamenevskiĭ; citation_volume=16; citation_issue=3; citation_publication_date=2004; citation_pages=56-98; citation_id=CR19 citation_journal_title=Trudy Moskov. Mat. Obšč; citation_title=Boundary value problems for elliptic equations in domains with conical or angular points; citation_author=VA Kondrat’ev; citation_volume=16; citation_publication_date=1967; citation_pages=209-292; citation_id=CR20 citation_title=Spectral Problems Associated with Corner Singularities of Solutions to Elliptic Equations, Mathematical Surveys and Monographs; citation_publication_date=2001; citation_id=CR21; citation_author=VA Kozlov; citation_author=VG Mazya; citation_author=J Rossmann; citation_publisher=American Mathematical Society citation_title=LNGFEM: graded meshes on domains of polygonal structures; citation_inbook_title=Recent Advances in Scientific Computing and Applications, Contemporary Mathematics; citation_publication_date=2013; citation_pages=239-246; citation_id=CR22; citation_author=H Li; citation_author=V Nistor; citation_publisher=American Mathematical Society citation_journal_title=Nonlinear Anal.; citation_title=The Dirichlet–Cauchy problem for nonlinear hyperbolic equations in a domain with edges; citation_author=VT Luong, NT Tung; citation_volume=125; citation_publication_date=2015; citation_pages=457-467; citation_doi=10.1016/j.na.2015.05.028; citation_id=CR23 citation_journal_title=Algebra i Analiz; citation_title=On dynamic problems in the theory of elasticity in domains with edges; citation_author=SI Matyukevich, BA Plamenevskiĭ; citation_volume=18; citation_issue=3; citation_publication_date=2006; citation_pages=158-233; citation_id=CR24 citation_title=Elliptic Equations in Polyhedral Domains, Mathematical Surveys and Monographs; citation_publication_date=2010; citation_id=CR25; citation_author=V Maz’ya; citation_author=J Rossmann; citation_publisher=American Mathematical Society citation_journal_title=J. Comput. Appl. Math.; citation_title=Finite elements with mesh refinement for wave equations in polygons; citation_author=F Müller, C Schwab; citation_volume=283; citation_publication_date=2015; citation_pages=163-181; citation_doi=10.1016/j.cam.2015.01.002; citation_id=CR26 citation_journal_title=Math. Methods Appl. Sci.; citation_title=Finite elements with mesh refinement for elastic wave propagation in polygons; citation_author=F Müller, C Schwab; citation_volume=39; citation_publication_date=2016; citation_pages=5027-5042; citation_doi=10.1002/mma.3355; citation_id=CR27 Müller, F.: Numerical analysis of finite element methods for second order wave equations in polygons. Ph.D. thesis, ETH Zürich, Diss. ETH No. 24385 (2017) citation_journal_title=SIAM J. Numer. Anal.; citation_title=Symmetric interior penalty discontinuous Galerkin methods for elliptic problems in polygons; citation_author=F Müller, D Schötzau, C Schwab; citation_volume=55; citation_issue=5; citation_publication_date=2017; citation_pages=2490-2521; citation_doi=10.1137/17M1120634; citation_id=CR29 citation_title=Theory of Adaptive Finite Element Methods: An Introduction, Multiscale, Nonlinear and Adaptive Approximation; citation_publication_date=2009; citation_id=CR30; citation_author=RH Nochetto; citation_author=KG Siebert; citation_author=A Veeser; citation_publisher=Springer citation_title=Mathematical Aspects of Discontinuous Galerkin Methods, Mathematics and Applications; citation_publication_date=2012; citation_id=CR31; citation_author=DA Pietro; citation_author=A Ern; citation_publisher=Springer citation_journal_title=Funktsional. Anal. i Prilozhen.; citation_title=On the wave equation in a cylinder with edges; citation_author=BA Plamenevskiĭ; citation_volume=32; citation_issue=1; citation_publication_date=1998; citation_pages=81-84; citation_doi=10.4213/faa405; citation_id=CR32 citation_title=Introduction à l’analyse numérique des equations aux derivées partielles; citation_publication_date=1998; citation_id=CR33; citation_author=P-A Raviart; citation_author=J-M Thomas; citation_publisher=Dunod citation_title=Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Problems: Theory and Implementation, Frontiers in Applied Mathematics; citation_publication_date=2008; citation_id=CR34; citation_author=B Rivière; citation_publisher=SIAM citation_journal_title=Mathematical Models and Methods in Applied Sciences; citation_title=Exponential convergence for hp-version and spectral finite element methods for elliptic problems in polyhedra; citation_author=Dominik Schötzau, Christoph Schwab; citation_volume=25; citation_issue=09; citation_publication_date=2015; citation_pages=1617-1661; citation_doi=10.1142/S0218202515500438; citation_id=CR35 citation_title= - and -FEM—Theory and Application to Solid and Fluid Mechanics; citation_publication_date=1998; citation_id=CR36; citation_author=C Schwab; citation_publisher=Oxford University Press citation_title=Triangle: engineering a 2D quality mesh generator and Delaunay triangulator; citation_inbook_title=Applied Computational Geometry: Towards Geometric Engineering. Lecture Notes in Computer Science; citation_publication_date=1996; citation_pages=203-222; citation_id=CR37; citation_author=JR Shewchuk; citation_publisher=Springer Wihler, T.P.: Discontinuous Galerkin FEM for Elliptic Problems in Polygonal Domains. Ph.D. thesis, Swiss Federal Institute of Technology Zurich, Diss. ETH No. 14973 (2002) citation_title=Partielle Differentialgleichungen: Sobolevräume und Randwertaufgaben. Mathematische Leitfäden; citation_publication_date=1982; citation_id=CR39; citation_author=J Wloka; citation_publisher=B. G. Teubner