Blockwise adaptivity for time dependent problems based on coarse scale adjoint solutions
2010 (English)In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 32, no 4, 2121-2145 p.Article in journal (Refereed) Published
We describe and test an adaptive algorithm for evolution problems that employs a sequence of "blocks" consisting of fixed, though non-uniform, space meshes. This approach offers the advantages of adaptive mesh refinement but with reduced overhead costs associated with load balancing, re-meshing, matrix reassembly, and the solution of adjoint problems used to estimate discretization error and the effects of mesh changes. A major issue whith a blockadaptive approach is determining block discretizations from coarse scale solution information that achieve the desired accuracy. We describe several strategies to achieve this goal using adjoint-based a posteriori error estimates and we demonstrate the behavior of the proposed algorithms as well as several technical issues in a set of examples.
Place, publisher, year, edition, pages
Society for Industrial and Applied Mathematics, 2010. Vol. 32, no 4, 2121-2145 p.
a posteriori error analysis, adaptive error control, adaptive mesh refinement, adjoint problem, discontinuous Galerkin method, duality, generalized Green's function, goal oriented error estiamtes, residual, variational analysis
Research subject Mathematics
IdentifiersURN: urn:nbn:se:umu:diva-33871DOI: 10.1137/090753826ISI: 000280771100020OAI: oai:DiVA.org:umu-33871DiVA: diva2:318490