On the Numerical Computation for Solving the Two-Dimensional Parabolic Equations by Space-Time Finite Element Method

Abstract

A space-time finite element method was presented for solving time-dependent and two-dimensional heat conduction problems. Linear hexadedron elements in a space-time domain were used as the finite elements. In this paper we present a discretization technique in which finite element approximations are used in time and space simultaneously for a relatively large time period called a time slab. The weighted residual process is used to formulate a finite element method for a space-time domain based upon the continuous Galerkin method. Numerical illustrations have indicated that the unstructured space-time algorithm provides more rapid convergence to the analytical solutions than the usual finite element analysis with discretization in space only.