Error Constants for the Semi-Discrete Galerkin Approximation of the Linear Heat Equation
| Autor: | Shin'ichi Oishi, Makoto Mizuguchi, Mitsuhiro T. Nakao, Kouta Sekine |
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| Rok vydání: | 2021 |
| Předmět: |
Numerical Analysis
Partial differential equation Applied Mathematics Weak solution General Engineering Omega Constant error Theoretical Computer Science Computational Mathematics Computational Theory and Mathematics Norm (mathematics) Convergence (routing) Applied mathematics Heat equation Galerkin method Software Mathematics |
| Zdroj: | Journal of Scientific Computing. 89 |
| ISSN: | 1573-7691 0885-7474 |
| DOI: | 10.1007/s10915-021-01636-3 |
| Popis: | In this paper, we propose $$L^2(J;H^1_0(\Omega ))$$ L 2 ( J ; H 0 1 ( Ω ) ) and $$L^2(J;L^2(\Omega ))$$ L 2 ( J ; L 2 ( Ω ) ) norm error estimates that provide the explicit values of the error constants for the semi-discrete Galerkin approximation of the linear heat equation. The derivation of these error estimates shows the convergence of the approximation to the weak solution of the linear heat equation. Furthermore, explicit values of the error constants for these estimates play an important role in the computer-assisted existential proofs of solutions to semi-linear parabolic partial differential equations. In particular, the constants provided in this paper are better than the existing constants and, in a sense, the best possible. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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