The Adaptive Finite Element Method For The P-Laplace Problem

The numerical solution of the nonlinear partial differential equation is a difficult problem with both extensive application background and challenge.As a typical nonlinear problem model,the numerical solution of the p-Laplace problem has attracted much attention.Firstly,we consider the adaptive finite element method(AFEM)for the p-Laplace problem.A posteriori and priori error analysis of conforming and nonconforming finite element method are measured in the new framework.A number of experiments confirm the effective convergence rates of the AFEM.In addition,we study the finite element method of parabolic p-Laplace problem.We introduce a new time-discrete scheme,so that the new error estimation of the equation can be divided.This estimate consists of two parts.In the first part,we calculate the error of the analytical solution of the original equation and the solution of the new iterative scheme.In the second part,we get the error of the solution of the new iterative scheme and the finite element solution of the original equation.This semi-implicit discrete scheme is unconditionally stable.