TY - GEN A1 - Jokar, Sadegh A1 - Mehrmann, Volker A1 - Pfetsch, Marc E. A1 - Yserentant, Harry T1 - Sparse Approximate Solution of Partial Differential Equations N2 - 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. KW - partial differential equation KW - sparse solution KW - dictionary KW - compressed sensing KW - restricted isometry property KW - mutual incoherence KW - hierarchical basis KW - linear programming Y1 - 2008 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/502 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-5028 ER -