Finite element method for one-dimensional and two-dimensional time dependent problems with B-splines

Abstract

One-dimensional and two-dimensional time dependent problems have been solved by the Galerkin method with cubic B-splines as basis functions. The redefining of basis functions has been done for two-dimensional problems, for the Dirichlet type boundary conditions, resulting in a non-homogeneous part in the approximation. The equidistribution of the error principle, given by Carl de Boor for one-dimensional problems, has been extended to two-dimensional problems. The solutions for nonlinear problems are obtained as the limit of solutions of a sequence of linear problems generated by the quasilinearization technique. The method developed with these features compares favourably with the methods available in literature.