On one approach to a posteriori error estimates for evolution problems solved by the method of lines

DOI10.1007/s002110100228zbMath0993.65103MaRDI QIDQ5946647

Pavel Šolín, Ivo M. Babuška, Miloslav Feistauer

Publication date: 11 April 2002

Published in: Numerische Mathematik (Search for Journal in Brave)

zbMATH Keywords

finite elementsnumerical examplesconvection-diffusion problemmethod of linesevolution equationsa posteriori error estimatesnonlinear parabolic problemsecond-order hyperbolic problem

Mathematics Subject Classification ID

Heat equation (35K05) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Initial value problems for second-order parabolic equations (35K15) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Initial value problems for second-order hyperbolic equations (35L15)

Related Items (14)

A posteriori error estimates for optimal distributed control governed by the evolution equations ⋮ Guaranteed a-posteriori error estimation for semi-discrete solutions of parabolic problems based on elliptic reconstruction ⋮ Space-time discontinuous Galerkin methods for weak solutions of hyperbolic linear symmetric Friedrichs systems ⋮ Interpolation error-based a posteriori error estimation for \(hp\)-refinement using first and second derivative jumps. ⋮ The method of lines for ternary diffusion problems ⋮ A posteriori error estimates of finite element method for the time-dependent Navier-Stokes equations ⋮ The impact of parameter selection on the performance of an automatic adaptive code for solving reaction-diffusion equations in three dimensions ⋮ A posteriori error estimation for the semidiscrete finite element method of parabolic differential equations ⋮ Adaptive space-time finite element methods for the wave equation on unbounded domains ⋮ A posteriorierror analysis of Euler-Galerkin approximations to coupled elliptic-parabolic problems ⋮ A posteriori error estimates for fully discrete nonlinear parabolic problems ⋮ Elliptic reconstruction and a posteriori error estimates for fully discrete linear parabolic problems ⋮ A Posteriori Error Estimates of Semidiscrete Mixed Finite Element Methods for Parabolic Optimal Control Problems ⋮ A posteriori error estimation with the \(p\)-version of the finite element method for nonlinear parabolic differential equations.

Uses Software

• DASSL

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