Parameter-free, weak imposition of Dirichlet boundary conditions and coupling of trimmed and non-conforming patches

Abstract

We present a parameter-free domain sewing approach for low-order as well as high-order finite elements. Its final form contains only primal unknowns; that is, the approach does not introduce additional unknowns at the interface. Additionally, it does not involve problem-dependent parameters, which require an estimation. The presented approach is symmetry preserving; that is, the resulting discrete form of an elliptic equation will remain symmetric and positive definite. It preserves the order of the underlying discretization, and we demonstrate high-order accuracy for problems of non-matching discretizations concerning the mesh size h as well as the polynomial degree of the order of discretization p. We also demonstrate how the method may be used to model material interfaces, which may be curved and for which the interface does not coincide with the underlying mesh. This novel approach is presented in the context of the p-version and B-spline version of the finite cell method, an embedded domain method of high order, and compared with more classical methods such as the penalty method or Nitsche's method.