Galerkin Method for a Non-Linear Parabolic Equation with Mixed Non-Linear Boundary Conditions,

摘要

Error estimates are derived for a numerical scheme for finding an approximate solution to nonlinear parabolic equations in the plane with mixed nonlinear boundary conditions. The scheme involves the Galerkin method coupled with successive substitutions and the Crank-Nicolson approximation. Problems of this type arise when considering unsteady,unsaturated flows in porous media.