On the a posteriori estimates for inverse operators of linear parabolic equations with applications to the numerical enclosure of solutions for nonlinear problems

DOI10.1007/s00211-013-0575-zzbMath1293.35062OpenAlexW2008377138WikidataQ59396255 ScholiaQ59396255MaRDI QIDQ2454037

Mitsuhiro T. Nakao, Takehiko Kinoshita, Takuma Kimura

Publication date: 12 June 2014

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

Full work available at URL: https://doi.org/10.1007/s00211-013-0575-z

zbMATH Keywords

Galerkin methodfull-discrete numerical scheme

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) A priori estimates in context of PDEs (35B45) Theoretical approximation in context of PDEs (35A35) 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 (9)

Rigorous numerics for nonlinear heat equations in the complex plane of time ⋮ Numerical verification for solutions to partial differential equations ⋮ A Method of Verified Computations for Solutions to Semilinear Parabolic Equations Using Semigroup Theory ⋮ Numerical Verification of Solutions for Nonlinear Parabolic 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 ⋮ Rigorous FEM for One-Dimensional Burgers Equation ⋮ Rigorous numerical inclusion of the blow-up time for the Fujita-type equation

Uses Software

• INTLAB

Cites Work

• On a posteriori estimates of inverse operators for linear parabolic initial-boundary value problems
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• Computer-assisted proofs for semilinear elliptic boundary value problems
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• On the best constant in the error bound for the \(H_0^1\)-projection into piecewise polynomial spaces
• Numerical existence and uniqueness proof for solutions of semilinear parabolic equations
• A numerical method to verify the invertibility of linear elliptic operators with applications to nonlinear problems
• Constructive A Priori Error Estimates for a Full Discrete Approximation of the Heat Equation
• On the Smoothing Property of the Galerkin Method for Parabolic Equations
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