The Optimal Convergence of the<i>h</i>‐<i>p</i>Version of the Finite Element Method with Quasi‐Uniform Meshes
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Abstract
In the framework of the Jacobi‐weighted Besov spaces, we analyze the convergence of the h‐p version of finite element solutions on quasi‐uniform meshes and the lower and upper bounds of errors for elliptic problems on polygons. Both lower and upper bounds are proved to be optimal in h and p, which leads to the optimal convergence of the h‐p version of the finite element method with quasi‐uniform meshes for elliptic problems on polygons. The results proved for the h‐p version include the h‐version with quasi‐uniform meshes and the p‐version with quasi‐uniform degrees as two special cases.
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
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