The element-free Galerkin method for the nonlinear p-Laplacian equation

The element-free Galerkin (EFG) method is developed in this paper for solving the nonlinear p-Laplacian equation. The moving least squares approximation is used to generate meshless shape functions, the penalty approach is adopted to enforce the Dirichlet boundary condition, the Galerkin weak form is employed to obtain the system of discrete equations, and two iterative procedures are developed to deal with the strong nonlinearity. Then, the computational formulas of the EFG method for the p-Laplacian equation are established. Numerical results are finally given to verify the convergence and high computational precision of the method.