Stability and performance of the SIPG and IIPG finite-element methods for wave propagation

Abstract

We consider two types of the interior penalty discontinuous Galerkin methods for wave propagation modeling: the symmetric interior penalty method (SIPG) and the incomplete interior penalty method (IIPG). The stability limit for explicit time stepping depends on the penalty parameter that imposes the continuity of the solution. For a given value of the penalty parameter, SIPG has a smaller stability limit and therefore requires smaller time steps than IIPG. IIPG, however, allows for a penalty term that is twice smaller than needed for SIPG, which results in a larger stability limit. In addition, IIPG requires less computations for the fluxes than SIPG. Numerical experiments show that this has the net effect of IIPG being more efficient than SIPG when considering the computational time required to obtain a solution with a given accuracy.