Constructive A Priori Error Estimates for a Full Discrete Approximation of the Heat Equation

DOI10.1137/120875661zbMath1293.65121OpenAlexW2055723554MaRDI QIDQ2845601

Takehiko Kinoshita, Takuma Kimura, Mitsuhiro T. Nakao

Publication date: 2 September 2013

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/3cd418ae866a6e4319558be905f044cbd098a01c

zbMATH Keywords

stabilityGalerkin methodslinear heat equationconstructive a priori error estimates

Mathematics Subject Classification ID

Heat equation (35K05) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

Related Items (12)

A Framework for the Numerical Computation and A Posteriori Verification of Invariant Objects of Evolution Equations ⋮ Improvement of the constructive a priori error estimates for a fully discretized periodic solution of heat equation ⋮ Numerical verification for solutions to partial differential equations ⋮ A Method of Verified Computations for Solutions to Semilinear Parabolic Equations Using Semigroup Theory ⋮ A posteriori error analysis of a fully-discrete finite element method for the wave equation ⋮ Numerical Verification of Solutions for Nonlinear Parabolic Problems ⋮ On the a posteriori estimates for inverse operators of linear parabolic equations with applications to the numerical enclosure of solutions for nonlinear problems ⋮ Error constants for the semi-discrete Galerkin approximation of the linear heat equation ⋮ Constructive error analysis of a full-discrete finite element method for the heat equation ⋮ Numerical verification for existence of a global-in-time solution to semilinear parabolic equations ⋮ Constructive error estimates for full discrete approximation of periodic solution for heat equation ⋮ Rigorous FEM for One-Dimensional Burgers Equation

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