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A Meyers type regularity result for approximations of second order elliptic operators by P1 finite elements |
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| Authors: | Nadine Badr Emmanuel Russ |
| Affiliation: | 1. Université Claude Bernard, Lyon I et CNRS UMR 5208, Batiment Doyen Jean Braconnier, 43 boulevard du 11 novembre 1918, , 69622 Villeurbanne Cedex, France;2. Université Joseph Fourier, Institut Fourier, UMR 5582, 100 rue des math, BP 74, , France |
| Abstract: | We prove a Meyers type regularity estimate for approximate solutions of second order elliptic equations obtained by P1 finite elements. The proofs rely on interpolation results for Sobolev spaces on graphs. Estimates for second order elliptic operators on rather general graphs are also obtained. |
| Keywords: | Elliptic operators elliptic equations interpolation Hö lder regularity Sobolev spaces graphs Galerkin methods 35J15 46B70 65M60 |