000133621 001__ 133621
000133621 005__ 20190603181631.0
000133621 0247_ $$2doi$$a10.1016/j.apnum.2008.12.001
000133621 022__ $$a0168-9274
000133621 037__ $$aARTICLE
000133621 245__ $$aAdaptive multiresolution schemes with local time stepping for two- dimensional degenerate reaction-diffusion systems
000133621 269__ $$a2009
000133621 260__ $$bElsevier$$c2009
000133621 336__ $$aJournal Articles
000133621 520__ $$aSpatially two-dimensional, possibly degenerate reaction–diffusion systems, with a focus on models of combustion, pattern formation and chemotaxis, are solved by a fully adaptive multiresolution scheme. Solutions of these equations exhibit steep gradients, and in the degenerate case, sharp fronts and discontinuities. This calls for a concentration of Computational effort on zones of strong variation. The multiresolution scheme is based on finite volume discretizations with explicit time stepping. The multiresolution representation of the solution is stored in a graded tree (“quadtree”), whose leaves are the non-uniform finite volumes on whose borders the numerical divergence is evaluated. By a thresholding procedure, namely the elimination of leaves with solution values that are smaller than a threshold value, substantial data compression and CPU time reduction is attained. The threshold value is chosen such that the total error of the adaptive scheme is of the same order as that of the reference finite volume scheme. Since chemical reactions involve a large range of temporal scales, but are spatially well localized (especially in the combustion model), a locally varying adaptive time stepping strategy is applied. For scalar equations, this strategy has the advantage that consistence with a CFL condition is always enforced. Numerical experiments with five different scenarios, in part with local time stepping, illustrate the effectiveness of the adaptive multiresolution method. It turns out that local time stepping accelerates the adaptive multiresolution method by a factor of two, while the error remains controlled.
000133621 6531_ $$aDegenerate parabolic equation
000133621 6531_ $$aAdaptive multiresolution scheme
000133621 6531_ $$aPattern formation
000133621 6531_ $$aFinite volume schemes
000133621 6531_ $$aChemotaxis
000133621 6531_ $$aKeller–Segel systems
000133621 6531_ $$aFlame balls interaction
000133621 6531_ $$aLocally varying time stepping
000133621 700__ $$aBendahmane, Mostafa
000133621 700__ $$aBürger, Raimund
000133621 700__ $$0242883$$g190276$$aRuiz-Baier, Ricardo
000133621 700__ $$aSchneider, Kai
000133621 773__ $$j59$$tApplied Numerical Mathematics$$k7$$q1668-1692
000133621 909C0 $$xU10797$$0252102$$pCMCS
000133621 909CO $$ooai:infoscience.tind.io:133621$$qGLOBAL_SET$$qSB$$particle
000133621 917Z8 $$x190276
000133621 937__ $$aCMCS-ARTICLE-2009-001
000133621 973__ $$rREVIEWED$$sPUBLISHED$$aOTHER
000133621 980__ $$aARTICLE