A Finite Element Method by Using Bivariate Splines for One Dimensional Heat Equations

Abstract

A finite element method by using bivariate splines (FB method) is proposed for solving one dimensional Heat Equations (HEs). Bivariate spline proper subspace of S 2;3 4 (∆ (2)) satisfying homogeneous boundary conditions on type-2 triangulations and quadratic B-spline interpolating boundary functions are primarily constructed. HEs are solved by the FB method. Numerical results reveal that the FB method is very effective and convenient.