A space-time Trefftz discontinuous Galerkin method for the acoustic wave equation in first-order formulation

DOI10.1007/s00211-017-0910-xzbMath1421.65026arXiv1610.08002OpenAlexW2734915834MaRDI QIDQ681701

Andrea Moiola, Ilaria Perugia

Publication date: 13 February 2018

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.08002

zbMATH Keywords

error estimatesacoustic wave equationTrefftz discontinuous Galerkin method

Mathematics Subject Classification ID

Wave equation (35L05) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Approximation by polynomials (41A10) Rate of convergence, degree of approximation (41A25)

Related Items (16)

Nonstandard finite element methods. Abstracts from the workshop held January 10--16, 2021 (hybrid meeting) ⋮ A Space-Time Trefftz Discontinuous Galerkin Method for the Linear Schrödinger Equation ⋮ On polynomial Trefftz spaces for the linear time-dependent Schrödinger equation ⋮ Tent-pitcher spacetime discontinuous Galerkin method for one-dimensional linear hyperbolic and parabolic PDEs ⋮ Global space-time Trefftz DG schemes for the time-dependent linear wave equation ⋮ Embedded Trefftz discontinuous Galerkin methods ⋮ Tent pitching and Trefftz-DG method for the acoustic wave equation ⋮ A space-time Trefftz DG scheme for the time-dependent Maxwell equations in anisotropic media ⋮ A space-time DG method for the Schrödinger equation with variable potential ⋮ A cVEM-DG space-time method for the dissipative wave equation ⋮ A discontinuous Galerkin time integration scheme for second order differential equations with applications to seismic wave propagation problems ⋮ A generalized inf-sup stable variational formulation for the wave equation ⋮ A roadmap for generalized plane waves and their interpolation properties ⋮ Coercive space-time finite element methods for initial boundary value problems ⋮ Space–time Trefftz-DG approximation for elasto-acoustics ⋮ A space–time quasi-Trefftz DG method for the wave equation with piecewise-smooth coefficients

Cites Work

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• Plane wave discontinuous Galerkin methods: exponential convergence of the \(hp\)-version
• Space-time discontinuous Galerkin discretizations for linear first-order hyperbolic evolution systems
• Non-dissipative space-time \(hp\)-discontinuous Galerkin method for the time-dependent Maxwell equations
• The equal spacing of \(N\) points on a sphere with application to partition-of-unity wave diffraction problems
• A discontinuous Galerkin method for linear symmetric hyperbolic systems in inhomogeneous media
• Transparent boundary conditions for a discontinuous Galerkin Trefftz method
• A multiple-direction Trefftz method for solving the multi-dimensional wave equation in an arbitrary spatial domain
• Discontinuous Galerkin finite element methods for second order hyperbolic problems
• A space-time finite element method for the wave equation
• Inverse acoustic and electromagnetic scattering theory.
• Extremal systems of points and numerical integration on the sphere
• Space-time finite element methods for elastodynamics: Formulations and error estimates
• A least-squares method for the Helmholtz equation
• A tent pitching scheme motivated by Friedrichs theory
• A space-time discontinuous Galerkin method for linearized elastodynamics with element-wise momentum balance
• Solution of the two-dimensional wave equation by using wave polynomials
• Proof of unconditional stability for a single-field discontinuous Galerkin finite element formulation for linear elastodynamics
• Discontinuous Galerkin methods with Trefftz approximations
• Spherical harmonics
• A Space-Time Discontinuous Galerkin Trefftz Method for Time Dependent Maxwell's Equations
• A hybrid discontinuous in space and time Galerkin method for wave propagation problems
• A Trefftz Polynomial Space-Time Discontinuous Galerkin Method for the Second Order Wave Equation
• A Survey of Trefftz Methods for the Helmholtz Equation
• PITCHING TENTS IN SPACE-TIME: MESH GENERATION FOR DISCONTINUOUS GALERKIN METHOD
• On Polynomial Approximation in Sobolev Spaces
• Plane Wave Discontinuous Galerkin Methods for the 2D Helmholtz Equation: Analysis of the p-Version
• The Cauchy Problem For Linear Partial Differential Equations With Restricted Boundary Conditions
• Retarded Potentials and Time Domain Boundary Integral Equations
• A space-time discontinuous Galerkin method for the solution of the wave equation in the time domain
• Vector potentials in three-dimensional non-smooth domains
• Explicit Finite Element Methods for Symmetric Hyperbolic Equations
• Application of an Ultra Weak Variational Formulation of Elliptic PDEs to the Two-Dimensional Helmholtz Problem
• Mapped Tent Pitching Schemes for Hyperbolic Systems
• A priorierror analysis of space–time Trefftz discontinuous Galerkin methods for wave problems
• A Basic Set of Homogeneous Harmonic Polynomials in k Variables

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