(untitled) (CSIAM Transactions on Applied Mathematics, 2020)
A continuous interior penalty finite element method (CIP-FEM) is proposed to solve high-frequency Helmholtz scattering problem by an impenetrable obstacle in two dimensions. To formulate the problem on a bounded domain, a Dirichlet-to-Neumann (DtN) boundary condition is proposed on the outer boundary by truncating the Fourier series of the original DtN mapping into finite terms. Assuming the truncation order N≥kR, where k is the wave number and R is the radius of the outer boundary, then the H^j-stabilities, j = 0,1,2, are established for both original and dual problems, with explicit and sharp estimates of the upper bounds with respect to k. Moreover, we prove that, when N≥λkR for some λ>1, the solution to the DtN-truncation problem converges exponentially to the original scattering problem as N increases. Under the condition that k^3h^2 is sufficiently small, we prove that the pre-asymptotic error estimates for the linear CIP-FEM as well as the linear FEM are C_1kh+C_2k^3h^2. Numerical experiments are presented to validate the theoretical results.