A framework for obtaining guaranteed error bounds for finite element approximations
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Publication:977381
DOI10.1016/j.cam.2010.01.037zbMath1191.65144OpenAlexW2072973709MaRDI QIDQ977381
Publication date: 22 June 2010
Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.cam.2010.01.037
numerical examplesdiscontinuous Galerkin methodPoisson equationguaranteed error boundsa posteriori error estimationnon-conforming finite element
Boundary value problems for second-order elliptic equations (35J25) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)
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Cites Work
- An optimal Poincaré inequality for convex domains
- Energy norm a posteriori error estimation for discontinuous Galerkin methods.
- A posteriori error estimates for a discontinuous Galerkin method applied to elliptic problems
- A posteriori error estimates for nonconforming finite element methods
- Robust a posteriori error estimation for the nonconforming Fortin--Soulie finite element approximation
- Fully Computable Error Bounds for Discontinuous Galerkin Finite Element Approximations on Meshes with an Arbitrary Number of Levels of Hanging Nodes
- Constant free error bounds for nonuniform order discontinuous Galerkin finite-element approximation on locally refined meshes with hanging nodes
- A Posteriori Error Estimation for Discontinuous Galerkin Finite Element Approximation
- A Posteriori Error Estimation for Lowest Order Raviart–Thomas Mixed Finite Elements
- Fully Computable Bounds for the Error in Nonconforming Finite Element Approximations of Arbitrary Order on Triangular Elements
- Conforming and nonconforming finite element methods for solving the stationary Stokes equations I
- A finite element method for domain decomposition with non-matching grids
- A Posteriori Error Estimates for a Discontinuous Galerkin Approximation of Second-Order Elliptic Problems
- Error Estimators for Nonconforming Finite Element Approximations of the Stokes Problem
- Element-oriented and edge-oriented local error estimators for nonconforming finite element methods
- A posteriori error estimators for nonconforming finite element methods
- Reliable a posteriori error control for nonconforming finite element approximation of Stokes flow
- Robust A Posteriori Error Estimation for Nonconforming Finite Element Approximation
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