Automatic weak imposition of free slip boundary conditions via Nitsche's method: application to nonlinear problems in geodynamics

Abstract

Imposition of free slip boundary conditions in science and engineering simulations presents a challenge when the simulation domain is non-trivial. Inspired by recent progress in symbolic computation of discontinuous Galerkin finite element methods, we present a symmetric interior penalty form of Nitsche's method to weakly impose these slip boundary conditions and present examples of its use in the Stokes subsystem motivated by problems in geodynamics. We compare numerical results with well established benchmark problems. We also examine performance of the method with iterative solvers.