Uniform error estimates of finite element method for a 3D semilinear elliptic problem with small viscosity

摘要

A finite element method based on P-1-element for the 3D semilinear elliptic boundary value problem with small viscosity is considered. The existence, uniqueness and uniform optimal H-1 and suboptimal L-2 error estimates of the finite element solution are provided, where 0 nu 1 = beta. Also, the numerical tests are made to show the efficiency of the error estimates of the finite element solution for the 3D semilinear elliptic boundary value problem with small viscosity. (C) 2018 Elsevier Inc. All rights reserved.