Weak Galerkin finite element method for solving one-dimensional coupled Burgers’ equations
In this paper, we apply a weak Galerkin method for solving one dimensional coupled Burgers’ equations. Based on a conservation form for nonlinear term and some of the technical derivational. Theorticly, we drive the optimal order error in \(L^2\) and \(H^1\) norm for both continuous and discrete time weak Galerkin finite element schemes, also the stability of continuous time weak Galerkin finite element method is proved. Numerically, the accuracy and effectiveness of the weak Galerkin finite element method are illustrated by using Numerical examples with the lower order Raviart–Thomas element \(RT_k\) for discrete weak derivative space.
KeywordsWeak Galerkin finite element method (WG-FEM) Burgers’ equations Optimal order
Mathematics Subject Classification65N15 65N30