Speaker
Alexey Chernov, Carl von Ossietzky Universität Oldenburg
Abstract
J. A. Nitsche’s idea of weakly enforcing boundary conditions through penalization inspired the development of several related approaches, including the discontinuous Galerkin Finite Element Methods (DGFEM) and the so‑called Nitsche’s mortaring technique for interface problems. In contrast to DG, where p- and hp-approximations on conforming (or 1-irregular) quasi-uniform and graded meshes are well-established, Nitsche’s nonconforming mortaring typically relies on h-type approximations. In this setting, the local polynomial degree remains fixed, and convergence is achieved through refinement of the FE mesh.
In this talk we extend our early results [1,2] and study the hp Nitsche’s mortaring in three contexts:
(a) quasiuniform meshes,
(b) meshes geometrically graded towards corner singularities,
(c) a symmetric Galerkin Boundary Element Method applied in conjunction with the FEM in two subdomains.
We study the numerical behaviour of these methods and establish a priori convergence estimates.
[1] A. Chernov, Nonconforming boundary elements and finite elements for interface and contact problems with friction – hp-version for mortar, penalty and Nitsche’s methods, PhD Thesis, University of Hannover, 2006
[2] A. Chernov and P. Hansbo, An hp-Nitsche’s method for interface problems with nonconforming unstructured finite element meshes, Vol. 76 of Lecture Notes in Computational Science and Engineering, pp. 153–162, Springer, 2011.