Consistent convergence rate estimates in the grid W2,02 (ω) norm for difference schemes approximating nonlinear elliptic equations with mixed derivatives and solutions from W2,0m (Ω), 3 < m ≤ 4

Abstract

The Dirichlet boundary value problem for nonlinear elliptic equations with mixed derivatives and unbounded nonlinearity is considered. A difference scheme for solving this class of problems and an implementing iterative process are constructed and investigated. The convergence of the iterative process is rigorously analyzed. This process is used to prove the existence and uniqueness of a solution to the nonlinear difference scheme approximating the original differential problem. Consistent with the smoothness of the desired solution, convergence rate estimates in the discrete norm of W_2,0² (ω) for difference schemes approximating the nonlinear equation with unbounded nonlinearity are established.