A high order discontinuous Galerkin Nitsche method for elliptic problems with fictitious boundary
In order to solve elliptic problems on domains with an immersed boundary representation on a structured grid, the authors use Nitche's method (concerning weak enforcement of Dirichlet boundary conditions) to formulate a discontinuous Galerkin method. The method avoids using very small elements on the boundary by associating them to a neighboring element with a sufficiently large intersection with the domain. Optimal order a priori error estimates are derived and illustrated by numerical examples for linear and quadratic bases. The numerical stability of the method is investigated by theoretical bounds on the condition number of the stiffness matrix. Numerical examples illustrate the implementation of the method.
scientific article; zbMATH DE number 6150055