Discretization of the wave equation using continuous elements in time and a hybridizable discontinuous Galerkin method in space

DOI10.1007/s10915-013-9741-9zbMath1296.65132OpenAlexW2087110602MaRDI QIDQ461231

Roland Griesmaier, Peter B. Monk

Publication date: 10 October 2014

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-013-9741-9

zbMATH Keywords

wave equationerror analysisdiscontinuous Galerkin methodhybridizationcontinuous time Galerkin method

Mathematics Subject Classification ID

Wave equation (35L05) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) 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)

Related Items (18)

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Uses Software

• RODAS

Cites Work

• Unnamed Item
• To CG or to HDG: A comparative study
• Error analysis for a hybridizable discontinuous Galerkin method for the Helmholtz equation
• High-order implicit hybridizable discontinuous Galerkin methods for acoustics and elastodynamics
• Galerkin and Runge-Kutta methods: unified formulation, a posteriori error estimates and nodal superconvergence
• A hybridizable discontinuous Galerkin method for Stokes flow
• Explicit local time-stepping methods for Maxwell's equations
• Solving Ordinary Differential Equations I
• Unified Hybridization of Discontinuous Galerkin, Mixed, and Continuous Galerkin Methods for Second Order Elliptic Problems
• A projection-based error analysis of HDG methods
• On the application of mixed finite element methods to the wave equations
• A Space-Time Finite Element Method for the Nonlinear Schrödinger Equation: The Continuous Galerkin Method
• A space-time finite element method for the nonlinear Schrödinger equation: the discontinuous Galerkin method
• Time Discretization of Parabolic Problems by the HP-Version of the Discontinuous Galerkin Finite Element Method
• Convergence of a continuous Galerkin method with mesh modification for nonlinear wave equations
• A continuous space-time finite element method for the wave equation
• The Mathematical Theory of Finite Element Methods

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