The Dual Mixed Finite Element Method for the Heat Diffusion Equation in a Polygonal Domain, I
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Abstract
The aim of this paper is to prove a priori error estimates for the semi-discrete solution of the dual mixed method for the heat diffusion equation in a polygonal domain. Due to the geometric singularities of the domain, the solution is not regular in the context of classical Sobolev spaces. Instead, one must use weighted Sobolev spaces. In order to recapture the optimal order of convergence, the meshes are refined in an appropriate fashion near the reentrant corners of the domain.
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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