Total error estimates of mixed finite element methods for nonlinear reaction-diffusion equations.

Abstract

[EN]We present some total error estimates of mixed finite element methods for parabolic problems with nonlinear diffusive and reactive terms. For the spatial discretization we use a mesh of rectangular elements with sides parallel to the axes, and standard Raviart-Thomas finite elements. Three temporal discrete schemes are studied, a completely implicit Euler scheme, a semi-implicit Euler scheme, and a completely explicit Euler scheme. As an application, we present some results of the explicit scheme with lowest order Raviart-Thomas finite elements for a model of natural combustion.