Sparse Approximate Solution of Partial Differential Equations
Please always quote using this URN:urn:nbn:de:0296-matheon-5028
- A new concept is introduced for the adaptive finite element discretization of partial differential equations that have a sparsely representable solution. Motivated by recent work on compressed sensing, a recursive mesh refinement procedure is presented that uses linear programming to find a good approximation to the sparse solution on a given refinement level. Then only those parts of the mesh are refined that belong to nonzero expansion coefficients. Error estimates for this procedure are refined and the behavior of the procedure is demonstrated via some simple elliptic model problems.
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| Author: | Sadegh Jokar, Volker Mehrmann, Marc E. Pfetsch, Harry Yserentant |
|---|---|
| URN: | urn:nbn:de:0296-matheon-5028 |
| Referee: | Peter Deuflhard |
| Document Type: | Preprint, Research Center Matheon |
| Language: | English |
| Date of first Publication: | 2008/03/26 |
| Release Date: | 2008/03/26 |
| Tag: | |
| Institute: | Technische Universität Berlin |
| Zuse Institute Berlin (ZIB) | |
| MSC-Classification: | 65-XX NUMERICAL ANALYSIS / 65Fxx Numerical linear algebra / 65F20 Overdetermined systems, pseudoinverses |
| 65-XX NUMERICAL ANALYSIS / 65Fxx Numerical linear algebra / 65F50 Sparse matrices | |
| 65-XX NUMERICAL ANALYSIS / 65Kxx Mathematical programming, optimization and variational techniques / 65K05 Mathematical programming methods [See also 90Cxx] | |
| 65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N50 Mesh generation and refinement | |
| Preprint Number: | 498 |
