Past Event: Oden Institute Seminar

Multilevel Norms for Negative Order Sobolev Spaces

Thomas Führer, Assistant Professor, Facultad de Matemáticas, Pontificia Universidad Católica de Chile

Abstract

In this talk, I present some recent results on multilevel decompositions of piecewise constants on simplicial meshes that are stable in negative order Sobolev spaces. Our findings can be applied to define local multilevel diagonal preconditioners that lead to bounded condition numbers (independent of the mesh-sizes and levels) and have optimal computational complexity. We discuss multilevel norms based on local (quasi-)projection operators that allow the efficient evaluation of negative order Sobolev norms. Finally, some extensions and possible further applications will conclude the talk. Bio since 07/2017 Assistant Professor position at Facultad de Matemáticas, Pontificia Universidad Católica de Chile 01/2017-06/2017 PostDoc position at Institute for Analysis and Scientific Computing, Vienna University of Technology 01/2015-10/2016 PostDoc position at Facultad de Matemáticas, Pontificia Universidad Católica de Chile 06/2014 Ph.D. graduation in Mathematics, Vienna University of Technology 03/2011 Bachelor of Science graduation in Technical Physics (B.Sc.), Vienna University of Technology 10/2010 Diploma in Technical Mathematics, Vienna University of Technology **Note: Please join this Zoom seminar online with the "Audio Only" function (no video)**