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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-toNeumann (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 k3h2 is sufficiently small, we prove that the preasymptotic error estimates for the linear CIP-FEM as well as the linear FEM are C1kh+C2k 3h2. Numerical experiments are presented to validate the theoretical results. AMS subject classifications: 65N12, 65N30, 78A40, 78A45

A CIP-FEM for High-Frequency Scattering Problem with the Truncated DtN Boundary Condition