Adaptive Finite Element Methods for Parabolic Problems V: Long-Time Integration

Abstract

We continue our previous work on adaptive finite element methods for parabolic problems, now with particular emphasis on long-time integration for semidefinite problems.MSC codes65N1565N30Keywordsparabolic problemslong-time integrationadaptive finite elementsa posteriori error estimateserror control

References

Page 1

	Year	Citations
Adaptive Finite Element Methods for Parabolic Problems I: A Linear Model Problem Kenneth Eriksson, Claes Johnson SIAM Journal on Numerical Analysis Numerical AnalysisFinite Element MethodMethod Of Fundamental SolutionNumerical ComputationEngineering	1991	610
Adaptive Finite Element Methods for Parabolic Problems IV: Nonlinear Problems Kenneth Eriksson, Claes Johnson SIAM Journal on Numerical Analysis Numerical AnalysisFinite Element MethodMethod Of Fundamental SolutionEngineeringPde-constrained Optimization	1995	220
Adaptive Finite Element Methods for Parabolic Problems II: Optimal Error Estimates in $L_\infty L_2 $ and $L_\infty L_\infty $ Kenneth Eriksson, Claes Johnson SIAM Journal on Numerical Analysis Numerical AnalysisFinite Element MethodOptimal Error EstimatesDiscretization ErrorEngineering	1995	213
Time discretization of parabolic problems by the discontinuous Galerkin method Kenneth Eriksson, Claes Johnson, Vidar Thomée ESAIM Mathematical Modelling and Numerical Analysis	1985	211
A Posteriori Error Bounds and Global Error Control for Approximation of Ordinary Differential Equations Donald Estep SIAM Journal on Numerical Analysis Numerical AnalysisFinite Element MethodEngineeringPde-constrained OptimizationPosteriori Error Bounds	1995	200
Finite Element Approximation of the Nonstationary Navier–Stokes Problem, Part II: Stability of Solutions and Error Estimates Uniform in Time John G. Heywood, Rolf Rannacher SIAM Journal on Numerical Analysis Numerical AnalysisFinite Element MethodNumerical Method For Partial Differential EquationEngineeringError Estimates Uniform	1986	160
Error Estimates and Adaptive Time-Step Control for a Class of One-Step Methods for Stiff Ordinary Differential Equations Claes Johnson SIAM Journal on Numerical Analysis Numerical AnalysisError EstimatesOne-step MethodsEngineeringNumerical Computation	1988	143
Numerics and Hydrodynamic Stability: Toward Error Control in Computational Fluid Dynamics Claes Johnson, Rolf Rannacher, Mats Boman SIAM Journal on Numerical Analysis Numerical AnalysisEngineeringFluid MechanicsAvailable Error AnalysisComputational Mechanics	1995	123

Page 1