Superconvergence of the Space-Time Continuous Finite Elements with Interpolated Coefficients for Semilinear Parabolic Problems
In this article, a space-time continuous finite element method with interpolated coefficients for a class of semilinear parabolic problem is introduced and analyzed. Basic global error estimates are established under the convergence assumption for linear problem. Further application of the orthogonal expansion method which is to construct some superapproximate interpolating functions, the supperconvergence on mesh nodes is proved. Finally the result is tested by a numerical example.
Z. G. Xiong et al., "Superconvergence of the Space-Time Continuous Finite Elements with Interpolated Coefficients for Semilinear Parabolic Problems", Advanced Materials Research, Vols. 314-316, pp. 1670-1675, 2011