A posteriori error estimation for the semidiscrete finite element method of parabolic differential equations

DOI10.1016/S0045-7825(00)00340-6zbMath1013.65099OpenAlexW1980883473MaRDI QIDQ5944616

Ivo M. Babuška, Stephan Ohnimus

Publication date: 17 June 2003

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0045-7825(00)00340-6

zbMATH Keywords

diffusion equationheat conductionfinite element methodsviscoelasticityplatea posteriori estimatesparabolic problemssemidiscrete approximations

Mathematics Subject Classification ID

Plates (74K20) Finite element methods applied to problems in solid mechanics (74S05) Heat equation (35K05) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Linear constitutive equations for materials with memory (74D05) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

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Cites Work

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• A posteriori error estimates for parabolic differential systems solved by the finite element method of lines
• A posteriori error estimation in finite element analysis
• Robust a posteriori error estimators for a singularly perturbed reaction-diffusion equation
• Adaptive finite elements for a linear parabolic problem
• Guaranteed computable bounds for the exact error in the finite element solution. I: One-dimensional model problem
• Anisotropic discretization- and model-error estimation in solid mechanics by local Neumann problems
• Adaptive Finite Element Methods for Parabolic Problems I: A Linear Model Problem
• An Adaptive Finite Element Method for Linear Elliptic Problems
• Error control of nonlinear evolution equations
• A posteriori error estimates for nonlinear problems:Lr, (0,T;W1,ρ (Ω))-error estimates for finite element discretizations of parabolic equations
• Practical aspects of a-posteriori estimation for reliable finite element analysis
• A POSTERIORIERROR ESTIMATION FOR THE FINITE ELEMENT METHOD-OF-LINES SOLUTION OF PARABOLIC PROBLEMS
• A Posteriori Error Estimation with Finite Element Semi- and Fully Discrete Methods for Nonlinear Parabolic Equations in One Space Dimension
• Validation of a posteriori error estimators by numerical approach
• A model study of element residual estimators for linear elliptic problems: The quality of the estimators in the interior of meshes of triangles and quadrilaterals
• Guaranteed computable bounds for the exact error in the finite element solution?Part II: bounds for the energy norm of the error in two dimensions
• On one approach to a posteriori error estimates for evolution problems solved by the method of lines

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