SDFEM for Time-Dependent Singularly Perturbed Boundary Turning Point Problem

A time-dependent singularly perturbed boundary turning point problem is considered. The numerical approximation to the solution of the problem is achieved by using a weighted-[Formula: see text] method on uniform mesh in time direction and streamline diffusion finite element method (SDFEM) on layer adapted mesh in space direction. Properties of the discrete Green’s functions are utilized to ensure [Formula: see text]-uniform stability and optimality of the SDFEM. We perform the convergence analysis for the proposed scheme both in space and time direction. The convergence results are obtained in the maximum norm by the decomposition of the solution into smooth and layer component. It is demonstrated that the proposed numerical scheme is [Formula: see text]-uniformly convergent of order one for ([Formula: see text]) and of almost order two for ([Formula: see text]). Some relevant numerical examples are taken to illustrate the theoretical findings and efficiency of the numerical method.