Dispersion Analysis Of The IPFEM For The Helmholtz Equation With High Wave Number On Equilateral Triangular Meshes

In this paper, we consider the selection of penalty parameter of the interior penalty finite element method for Helmholtz equation with high wave number. We know when the wave number is large, the ordinary finite element method suffers the effects of pollution, namely, the ratio between the error of finite element solution in H1-norm and the error of the best approximation from the finite element space increases as k increases. For example, the order of pollution error of linear finite element solution in H1-norm is O(k3h2). We consider the linear IPFEM on equilateral triangular meshes. By the dispersion analysis, it is proved that by choosing appropriate penalty parameter, the phase difference of the IPFEM solution can be reduced to be of order O(k5h4). Numerical experiments show that the selection of penalty parameter can significantly reduce the H1 error of the interior penalty finite element solution.