Explicit error bounds in a conforming finite element method
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Publication:4257682
DOI10.1090/S0025-5718-99-01093-5zbMath0929.65095MaRDI QIDQ4257682
Brigitte Métivet, Philippe Destuynder
Publication date: 31 August 1999
Published in: Mathematics of Computation (Search for Journal in Brave)
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
- Toward a universal h-p adaptive finite element strategy. III: Design of h-p meshes
- A family of higher order mixed finite element methods for plane elasticity
- A unified approach to a posteriori error estimation using element residual methods
- A posteriori error estimation and adaptive mesh-refinement techniques
- Some A Posteriori Error Estimators for Elliptic Partial Differential Equations
- Error Estimate Procedure in the Finite Element Method and Applications
- Finite Element Methods for Navier-Stokes Equations
- A simple error estimator and adaptive procedure for practical engineerng analysis
- An Adaptive Finite Element Method for Linear Elliptic Problems
- The superconvergent patch recovery anda posteriori error estimates. Part 1: The recovery technique
- Error Estimates for Adaptive Finite Element Computations
- The problem of the selection of an a posteriori error indicator based on smoothening techniques
- Superconvergence in Finite Element Methods and Meshes That are Locally Symmetric with Respect to a Point
- Approximations in elasticity based on the concept of function space
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