On the numerical analysis of a nonlinear elliptic problem via mixed-FEM and Lagrange multi\-pliers.
type: Item
instance of: scholarly article
title: On the numerical analysis of a nonlinear elliptic problem via mixed-FEM and Lagrange multi\-pliers.
zbMATH Open document ID: 1047.65098
author: Tomás P. Barrios
author: Gabriel N. Gatica
author: Luis F. Gatica
published in: Applied Numerical Mathematics
publication date: 2004-03-14T00:00:00Z
review text: The paper deals with mixed finite elements for solving nonlinear second-order elliptic problems. The theoretical results extend previous ones with respect to stronger nonlinearities and mixed boundary conditions. Rigorous mathematical proofs show that the variational formulation and the associated discrete problem are well posed and a priori error estimates are derived. Also an a posteriori error analysis is provided which serves as the basis for adaptive grid refinement. Numerical results for two simple test cases are presented which confirm the theoretical results. In particular, a comparison with computations with uniform refinement illustrate the advantages of the adaptive approach.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 65N50
zbMATH DE Number: 2055525
zbMATH Keywords: mixed boundary conditions
zbMATH Keywords: mixed finite elements
zbMATH Keywords: Raviart-Thomas spaces
zbMATH Keywords: local problems
zbMATH Keywords: nonlinear second-order elliptic problems
zbMATH Keywords: a priori error estimates
zbMATH Keywords: adaptive grid refinement
zbMATH Keywords: numerical results
describes a project that uses: BL2D-V2
MaRDI profile type: Publication
full work available at URL: j.apnum.2003.08.001
OpenAlex ID: W2014450622
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DOI: 10.1016/J.APNUM.2003.08.001
description: scientific article; zbMATH DE number 2055525