Constructive error analysis of a full-discrete finite element method for the heat equation

DOI10.1007/s13160-019-00362-6zbMath1427.65216arXiv1806.07054OpenAlexW3099531546MaRDI QIDQ2009472

Mitsuhiro T. Nakao, Takuma Kimura, Kouji Hashimoto, Teruya Minamoto

Publication date: 28 November 2019

Published in: Japan Journal of Industrial and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.07054

zbMATH Keywords

heat equationfinite element methodconstructive error analysis

Mathematics Subject Classification ID

Heat equation (35K05) A priori estimates in context of PDEs (35B45) 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 (2)

Numerical Verification of Solutions for Nonlinear Parabolic Problems ⋮ Error constants for the semi-discrete Galerkin approximation of the linear heat equation

Uses Software

• INTLAB

Cites Work

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• A posteriori estimates of inverse operators for initial value problems in linear ordinary differential equations
• Solving nonlinear parabolic problems with result verification. I: One- space dimensional case
• On the best constant in the error bound for the \(H_0^1\)-projection into piecewise polynomial spaces
• On the a posteriori estimates for inverse operators of linear parabolic equations with applications to the numerical enclosure of solutions for nonlinear problems
• Constructive A Priori Error Estimates for a Full Discrete Approximation of the Heat Equation

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