The semi discrete formulation of Galerkin and Galerkin-conservation finite element methods for two dimensional coupled burgers' problem

Abstract EN

In this paper, the semi discrete formulation of Galerkin and Galerkin-Conservation (G and G-C) finite element methods are used to approximate the solution of the coupled Burgers' problem.

The theoretical evidence proved that the property of the bilinear form ? (?,?) (v-elliptic and continuity) and the stability of both schemes, also we proved that the error estimate of these methods are of ? (ℎ).

We used the artificial diffusion method to improve the analytics solution of the problem and the approximate solution when (∈ < ℎ).

Numerical example is tested to illustrate these schemes and the numerical results by using ODE 15s, ordinary differential equation, solvers matlab are compared with the exact solution.