Treatment of the radiation boundary condition at infinity is of great significance for wave analyses in unbounded coastal domains. The higher order infinite element for the finite element method is newly developed in order to improve accuracy rather than that by the linear infinite element presented in this series of researches. The shape functions for function variation are third-order polynomials in the radial coordinate and the variation in the angular coordinate is linear. The element has three novel features. First, the mapping for function variation is able to perform the radiation boundary condition up to r-^3m, r being the radial distance and m = 1/2 for wave problems. The second feature is easiness in connecting the infinite element to the interior, standard elements. The third one is an integrable feature over the element with the aid of the infinite mapping. As a test of the new, third-order infinite element, the problem of wave diffraction by a cylinder is solved, along with a comparison with the analytical solution and with numerical results obtained using other finite elements. Numerical error assessment shows efficiency of the new infinite element.
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