A posteriori error estimation for variational problems with uniformly convex functionals

DOI10.1090/S0025-5718-99-01190-4zbMath0949.65070MaRDI QIDQ4942775

Sergey I. Repin

Publication date: 15 March 2000

Published in: Mathematics of Computation (Search for Journal in Brave)

zbMATH Keywords

Banach spacesvariational problemsduality theorybounded linear operatora posteriori error estimationuniformly convex functional

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Existence theories for problems in abstract spaces (49J27)

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Cites Work

• Adaptive finite element methods in computational mechanics
• The superconvergent patch recovery (SPR) and adaptive finite element refinement
• A posteriori error analysis in finite elements: The element residual method for symmetrizable problems with applications to compressible Euler and Navier-Stokes equations
• A posteriori error estimation for nonlinear variational problems by duality theory
• The stability in L\(^q\) of the L\(^2\)-projection into finite element function spaces
• A unified approach to a posteriori error estimation using element residual methods
• A posteriori error estimation for elasto-plastic problems based on duality theory
• A priori error estimates of variational-difference methods for Hencky plasticity problems
• Error estimates for stresses in the finite element analysis of the two-dimensional elasto-plastic problems
• A posteriori error estimates for approximate solutions of variational problems with functionals of power growth
• An a Posteriori Error Estimate and Adaptive Timestep Control for a Backward Euler Discretization of a Parabolic Problem
• Some A Posteriori Error Estimators for Elliptic Partial Differential Equations
• The self-equilibration of residuals and complementarya posteriori error estimates in the finite element method
• Error Estimate Procedure in the Finite Element Method and Applications
• A simple error estimator and adaptive procedure for practical engineerng analysis
• The Stability in L p and W p 1 of the L 2 -Projection onto Finite Element Function Spaces
• An Adaptive Finite Element Method for Linear Elliptic Problems
• A Posteriori Error Analysis of Finite Element Solutions for One-Dimensional Problems
• A‐posteriori error estimates for the finite element method
• Error Estimates for Adaptive Finite Element Computations
• A posteriori error estimation for nonlinear variational problems
• ERRORS OF FINITE ELEMENT METHOD FOR PERFECTLY ELASTO-PLASTIC PROBLEMS
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