A new embedding result for Kondratiev spaces and application to adaptive approximation of elliptic PDEs
| Autor: | Hansen, Markus |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2014 |
| Předmět: |
Triebel-Lizorkin spaces
Wavelet decomposition Besov regularity FINITE-ELEMENTE-METHODE (NUMERISCHE MATHEMATIK) FOS: Mathematics Adaptive Finite element approximation ELLIPTIC DIFFERENTIAL EQUATIONS (MATHEMATICAL ANALYSIS) Kondratiev spaces ddc:510 STABILITÄT PARTIELLER DIFFERENTIALGLEICHUNGEN (ANALYSIS) NONLINEAR APPROXIMATION (MATHEMATICAL ANALYSIS) Parametric elliptic problems POLYTOPES + POLYHEDRA (GEOMETRY) NICHTLINEARE APPROXIMATION (ANALYSIS) ELLIPTISCHE DIFFERENTIALGLEICHUNGEN (ANALYSIS) WAVELETS + WAVELET TRANSFORMATIONS (MATHEMATICAL ANALYSIS) WAVELETS + WAVELET-TRANSFORMATIONEN (ANALYSIS) Regularity for elliptic PDEs n-term approximation POLYTOPE + POLYEDER (GEOMETRIE) FINITE ELEMENT METHOD (NUMERICAL MATHEMATICS) STABILITY OF PARTIAL DIFFERENTIAL EQUATIONS (MATHEMATICAL ANALYSIS) Mathematics |
| Zdroj: | Research Report, 2014-30 (30) |
| DOI: | 10.3929/ethz-a-010386160 |
| Popis: | In a continuation of recent work on Besov regularity of solutions to elliptic PDEs in Lipschitz domains with polyhedral structure, we prove an embedding between weighted Sobolev spaces (Kondratiev spaces) relevant for the regularity theory for such elliptic problems, and Triebel- Lizorkin spaces, which are known to be closely related to approximation spaces for nonlinear n-term wavelet approximation. Additionally, we also provide necessary conditions for such embeddings. As a further application we discuss the relation of these embedding results with results by Gaspoz and Morin for approximation classes for adaptive Finite element approximation, and subsequently apply these result to parametric problems. Research Report, 2014-30 (30) |
| Databáze: | OpenAIRE |
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