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

Authors:
Luis Ferragut;Isabel Asensio
Affiliations:
Department of Applied Mathematics, University of Salamanca, pza Merced s.n. 37008-Salamanca, Spain;Department of Applied Mathematics, University of Salamanca, pza Merced s.n. 37008-Salamanca, Spain
Venue:
Neural, Parallel & Scientific Computations
Year:
2002

Citing 3
Cited 1

A Nonlinear Mixed Finite Eelement Method for a Degenerate Parabolic Equation Arising in Flow in Porous Media

SIAM Journal on Numerical Analysis
Solution of Parabolic Equations by Backward Euler-Mixed Finite Element Methods on a Dynamically Changing Mesh

SIAM Journal on Numerical Analysis
Analysis of Expanded Mixed Finite Element Methods for a Nonlinear Parabolic Equation Modeling Flow into Variably Saturated Porous Media

SIAM Journal on Numerical Analysis

A wildland fire model with data assimilation

Mathematics and Computers in Simulation

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Abstract

A mixed finite element approximation is presented for a class of non-linear reaction diffusion 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 diffusive term and demostrated with a new technique. The proofs of this error estimates are described in detail, first in the dual norm, and then in the L2-norm. As an application, a model for numerically simulating wildland fires is presented.