An Arbitrary Order Reconstructed Discontinuous Approximation to Biharmonic Interface Problem

Abstract

We present an arbitrary order discontinuous Galerkin finite element method for solving the biharmonic interface problem on the unfitted mesh. The approximation space is constructed by a patch reconstruction process with at most one degrees of freedom per element. The discrete problem is based on the symmetric interior penalty method and the jump conditions are weakly imposed by the Nitsche’s technique. The $C^2$-smooth interface is allowed to intersect elements in a very general fashion and the stability near the interface is naturally ensured by the patch reconstruction. We prove the optimal a priori error estimate under the energy norm and the $L^2$ norm. Numerical results are provided to verify the theoretical analysis.