Convergence of a Full Discretization of Quasi-linear Parabolic Equations in Isotropic and Anisotropic Orlicz Spaces

Abstract. Convergence of a full discretization is shown for a general class of nonlinear parabolic November 10, 2011 problems. The numerical method combines the backward Euler method for the time discretization with a generalized internal approximation scheme for the spatial discretization. The governing monotone elliptic differential operator is described by a nonlinearity that may have anisotropic and non-polynomial growth but fulfills a coercivity condition in terms of a generalized N -function.