A posteriori estimates of inverse operators for boundary value problems in linear elliptic partial differential equations

DOI10.1090/S0025-5718-2013-02676-2zbMath1280.65119OpenAlexW2049098928MaRDI QIDQ2840620

Yoshitaka Watanabe, Takehiko Kinoshita, Mitsuhiro T. Nakao

Publication date: 23 July 2013

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-2013-02676-2

zbMATH Keywords

numerical experimentsGalerkin approximationlinear elliptic partial differential equationconstructive a posteriori estimates

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) A priori estimates in context of PDEs (35B45)

Related Items (10)

A Framework for the Numerical Computation and A Posteriori Verification of Invariant Objects of Evolution Equations ⋮ Norm bound computation for inverses of linear operators in Hilbert spaces ⋮ Some improvements of invertibility verifications for second-order linear elliptic operators ⋮ A new formulation using the Schur complement for the numerical existence proof of solutions to elliptic problems: without direct estimation for an inverse of the linearized operator ⋮ An alternative approach to norm bound computation for inverses of linear operators in Hilbert spaces ⋮ Some Remarks on the Rigorous Estimation of Inverse Linear Elliptic Operators ⋮ Some lower bound estimates for resolvents of a compact operator on an infinite-dimensional Hilbert space ⋮ An improved method for verifying the existence and bounds of the inverse of second-order linear elliptic operators mapping to dual space ⋮ Inverse norm estimation of perturbed Laplace operators and corresponding eigenvalue problems ⋮ Some considerations of the invertibility verifications for linear elliptic operators

Uses Software

• INTLAB

Cites Work

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