University of Texas at Austin

Past Event: Oden Institute Seminar

Conforming Galerkin Schemes Via Traces and Applications to Plate Bending

Norbert Heuer, Professor, Department of Mathematics, Pontificia Universidad Católica de Chile

3:30 – 5PM
Tuesday Oct 6, 2020

Zoom Meeting

Abstract

In recent years the DPG method has raised some attention. It is a discontinuous Petrov-Galerkin method where the selection of special test functions guarantees discrete stability. In this way, for a given well-posed problem, any well-posed variational formulation is appropriate to set up a Galerkin approximation. Practical and theoretical reasons suggest to use ultraweak variational formulations. In this case, field variables are considered in L_2 so that test functions carry all the appearing derivatives. Transferring derivatives to test functions by integrating by parts, this gives rise to trace terms and thus, trace operators. In the ultraweak case, trace operators carry all the regularity weight of the problem. They have to be defined in appropriate spaces with corresponding images. They also carry the burden of conformity, when and where wanted. Independently of the ultraweak formulation and implied DPG scheme, the conformity of trace approximations is essential to understand and characterize the conformity of Galerkin schemes in general. We discuss this relation, and strategies and arising difficulties of this approach in the case of plate bending models. Bio Phd 1992, Habilitation 1998, both at University of Hanover, Germany 1992-2000 Research Associate at U of Bremen, Germany 2000-2004 Full Professor at U of Concepcion, Chile 2004-2008 Full Professor at Brunel University, UK since 2008 Full Professor at Pontical Catholic University of Chile **Note: Please join this Zoom seminar online with the "Audio Only" function (no video)**
Conforming Galerkin Schemes Via Traces and Applications to Plate Bending

Event information

Date
3:30 – 5PM
Tuesday Oct 6, 2020
Location Zoom Meeting
Hosted by Leszek F. Demkowicz