Galerkin Finite Element Method by Using Bivariate Splines for Parabolic PDEs

Abstract

A Galerkin finite element method by using bivariate splines (GB method) is proposed for solving parabolic partial differential equations (PPDEs). Bivariate spline proper subspace of $S_4^{2,3}(\Delta_{mn}^{(2)})$ satisfying homogeneous boundary conditions on type-2 triangulations and quadratic B-spline interpolating boundary functions are primarily constructed. PPDEs are solved by the GB method.