Numerical Analysis Seminar

Date: November 1, 2017

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Natalia Kopteva, University of Limerick, Ireland

Title: Fully computable a posteriori error estimators on anisotropic meshes

Abstract: It is well known that anisotropic meshes offer an efficient way of computing reliable numerical approximations of solutions that exhibit sharp boundary and interior layers. Our goal is to give explicitly and fully computable a posteriori error estimates on reasonably general anisotropic meshes in the energy norm. This goal is achieved by a certain combination of explicit flux reconstruction and flux equilibration. Our approach differs from the previous work, mostly done for shape-regular meshes, in a few ways. The fluxes are equilibrated within a local patch using anisotropic weights depending on the local, possibly anisotropic, mesh geometry. Prior to the flux equilibration, divergence-free corrections are introduced for pairs of anisotropic triangles sharing a short edge. We shall also give an upper bound for the constructed estimator, in which the error constant is independent of the diameters and the aspect ratios of mesh elements, and discuss the efficiency of a posteriori error estimators on anisotropic meshes.