Abstract:

The discontinuous Galerkin finite element approximation schemes for the Extended Fisher-Kolmogorov (EFK) equation are studied by using the Wilson element. Without using the technique of postprocessing technique, the convergence results with order $O(h^{2})/O(h^{2}+\tau)$ for the primitive solution $u$ and intermediate variable $v=-\triangle u$ are obtained for the semi-discrete and linearized Euler fully discrete approximation schemes respectively through a new splitting technique for the nonlinear terms. The above results are just one order higher than the usual error estimates of the Wilson element. Here, $h$ and $\tau$ are parameters of the subdivision in space and time step, respectively.

Key words: EFK equation, Discontinuous Galerkin finite element, Wilson element, Semi-discrete and fully-discrete schemes, Convergence