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

DOI10.1007/s00211-020-01155-7zbMath1456.65035arXiv1910.00759OpenAlexW3094361996MaRDI QIDQ2217873

Kouta Sekine, Shin'ichi Oishi, Mitsuhiro T. Nakao

Publication date: 11 January 2021

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

Full work available at URL: https://arxiv.org/abs/1910.00759

zbMATH Keywords

Schur complementpartial differential equationselliptic problemnonlinear problemexistence result

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical solutions to equations with linear operators (65J10)

Related Items (4)

Efficient approaches for verifying the existence and bound of inverse of linear operators in Hilbert spaces ⋮ A numerical proof algorithm for the non-existence of solutions to elliptic boundary value problems ⋮ Inverse norm estimation of perturbed Laplace operators and corresponding eigenvalue problems ⋮ Computer-assisted proof for the stationary solution existence of the Navier-Stokes equation over 3D domains

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