A stabilized Nitsche cut element method for the wave equation

Abstract

We give a weak formulation for solving the wave equation (ü=∇2u+f) on a 2-dimensional immersed domain. In the spatial finite element discretization, boundaries do not conform to element boundaries. Dirichlet and Neumann boundary conditions are enforced weakly by Nitsche’s method. Additional penalty terms act on the gradient jumps over the interior faces of the elements cut by the boundary. These terms ensure a non-stiff temporal system, which makes it possible to perform explicit time stepping. We give optimal a priori error estimates: second order accuracy for u−uh and u̇−u̇h, and first order accuracy for ∇(u−uh) in L2-norm. Numerical results verify this.