A posteriori discontinuous finite element error estimation for two-dimensional hyperbolic problems.
From MaRDI portal
Publication:1871033
DOI10.1016/S0045-7825(02)00502-9zbMath1062.65091MaRDI QIDQ1871033
Thomas C. Massey, Slimane Adjerid
Publication date: 6 May 2003
Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)
finite element methoderror analysisdiscontinuous Galerkin methodlinear scalar hyperbolic equationsquasilinear scalar hyperbolic equations
First-order nonlinear hyperbolic equations (35L60) 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) Initial value problems for first-order hyperbolic systems (35L45)
Related Items
A superconvergent local discontinuous Galerkin method for the second-order wave equation on Cartesian grids, A discontinuous Galerkin method for higher-order ordinary differential equations, Superconvergence and a posteriori error estimates for the LDG method for convection-diffusion problems in one space dimension, Superconvergence of discontinuous Galerkin solutions for a nonlinear scalar hyperbolic problem, A posteriori error estimation for the method of lumped masses applied to second-order hyperbolic problems, Asymptotically exact a posteriori local discontinuous Galerkin error estimates for the one-dimensional second-order wave equation, A posteriori error analysis of the discontinuous Galerkin method for two-dimensional linear hyperbolic conservation laws on Cartesian grids, Superconvergence and \textit{a posteriori} error estimates of the DG method for scalar hyperbolic problems on Cartesian grids, A posteriori error estimates and adaptivity for the discontinuous Galerkin solutions of nonlinear second-order initial-value problems, An adaptive finite element method for high-frequency scattering problems with smoothly varying coefficients, A superconvergent local discontinuous Galerkin method for elliptic problems, The discontinuous Galerkin method for two-dimensional hyperbolic problems. II: A posteriori error estimation, Superconvergence of discontinuous Galerkin methods for convection-diffusion problems, A posteriori error estimate for discontinuous Galerkin finite element method on polytopal mesh, A posteriori discontinuous Galerkin error estimation on tetrahedral meshes, Discontinuous Galerkin error estimation for hyperbolic problems on unstructured triangular meshes, A discontinuous Galerkin method for the wave equation, A superconvergent discontinuous Galerkin method for hyperbolic problems on tetrahedral meshes, The local discontinuous Galerkin method for the fourth-order Euler-Bernoulli partial differential equation in one space dimension. I: Superconvergence error analysis, Asymptotically exact discontinuous Galerkin error estimates for linear symmetric hyperbolic systems, A posteriori error analysis of the discontinuous finite element methods for first order hyperbolic problems, Discontinuous Galerkin error estimation for linear symmetric hyperbolic systems, The local discontinuous Galerkin method for the fourth-order Euler-Bernoulli partial differential equation in one space dimension. II: A posteriori error estimation, Numerical resolution of discontinuous Galerkin methods for time dependent wave equations, The discontinuous Galerkin method for two-dimensional hyperbolic problems. I: Superconvergence error analysis, Error Control for Discontinuous Galerkin Methods for First Order Hyperbolic Problems, Superconvergence of bi-k Degree Time-Space Fully Discontinuous Finite Element for First-Order Hyperbolic Equations, Asymptotically exact a posteriori LDG error estimates for one-dimensional transient convection-diffusion problems, Discontinuous Galerkin error estimation for linear symmetrizable hyperbolic systems, The highest superconvergence analysis of ADG method for two point boundary values problem, \textit{A posteriori} error estimates for a discontinuous Galerkin method applied to one-dimensional nonlinear scalar conservation laws, Superconvergence of the local discontinuous galerkin method applied to the one‐dimensional second‐order wave equation, Superconvergence of discontinuous finite element solutions for transient convection-diffusion problems, High-order RKDG methods for computational electromagnetics, Asymptotically exact a posteriori error estimates for a one-dimensional linear hyperbolic problem, Two efficient and reliable a posteriori error estimates for the local discontinuous Galerkin method applied to linear elliptic problems on Cartesian grids, Superconvergence of the local discontinuous Galerkin method for the sine-Gordon equation on Cartesian grids, A posteriori local discontinuous Galerkin error estimation for two-dimensional convection-diffusion problems, Superconvergence of the space-time discontinuous Galerkin method for linear nonhomogeneous hyperbolic equations, An easily computable error estimator in space and time for the wave equation, Development of an adaptive discontinuous-Galerkin finite element method for advection-reaction equations, Even-odd goal-oriented a posteriori error estimation for elliptic problems, Superconvergence of Discontinuous Galerkin Methods for Two-Dimensional Hyperbolic Equations, A posteriori finite element error estimation for second-order hyperbolic problems.
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations
- TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. III: One-dimensional systems
- A discontinuous \(hp\) finite element method for convection-diffusion problems
- Parallel, adaptive finite element methods for conservation laws
- A posteriori error estimation for discontinuous Galerkin solutions of hyperbolic problems
- \(hp\)-version discontinuous Galerkin methods for hyperbolic conservation laws
- Error estimation for discontinuous Galerkin solutions of two-dimensional hyperbolic problems
- A parallel \(hp\)-adaptive discontinuous Galerkin method for hyperbolic conservation laws
- Parallel adaptive \(hp\)-refinement techniques for conservation laws
- Discontinuous Galerkin methods. Theory, computation and applications. 1st international symposium on DGM, Newport, RI, USA, May 24--26, 1999
- TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework
- An Elliptic Collocation-Finite Element Method with Interior Penalties
- Adaptive Finite Element Methods for Parabolic Problems II: Optimal Error Estimates in $L_\infty L_2 $ and $L_\infty L_\infty $
- hp‐version discontinuous Galerkin methods for hyperbolic conservation laws: A parallel adaptive strategy
- Error Estimates for Finite Element Methods for Scalar Conservation Laws