Mixed finite element methods for a class of nonlinear reaction diffusion problems

Abstract

[EN]A mixed finite element approximation is presented for a class of nonlinear reaction difusion problems with a wide applicability. Some results about the existence and uniqueness of weak solutions are resumed. Semidiscrete error estimates are established assuming only Lipschitz regularity of the reactive term and nondecreasing of the difusive term and demostrated with a new technique. The proofs of this error estimates are described in detail, ¯rst in the dual norm, and then in the L2-norm. As an application, a model for numerically simulating wildland fires is presented.