Superconvergence of triangular quadratic finite element with interpolated coefficients for semilinear parabolic equation

To solve spatially semidiscrete finite element solution of semilinear parabolic equation, the triangular quadratic finite element method with interpolated coefficients (ICFEM) is introduced and analyzed. Based on a class of the orthogonal expansion in triangle, it is shown that ICFEM has superconvergence O(h4) at each vertex and at the side midpoint of all triangles, which is similar to that of semilinear elliptic problems.