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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

   

 

A mimetic discretization of elliptic obstacle problems


Authors: Paola F. Antonietti, Lourenco Beirão da Veiga and Marco Verani
Journal: Math. Comp. 82 (2013), 1379-1400
MSC (2010): Primary 65N30; Secondary 35R35
Published electronically: February 20, 2013
MathSciNet review: 3042568
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Abstract: We develop a Finite Element Method (FEM) which can adopt very general meshes with polygonal elements for the numerical approximation of elliptic obstacle problems. These kinds of methods are also known as mimetic discretization schemes, which stem from the Mimetic Finite Difference (MFD) method. The first-order convergence estimate in a suitable (mesh-dependent) energy norm is established. Numerical experiments confirming the theoretical results are also presented.


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Additional Information

Paola F. Antonietti
Affiliation: MOX, Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133 Milano, Italy
Email: paola.antonietti@polimi.it

Lourenco Beirão da Veiga
Affiliation: Dipartimento di Matematica, Università di Milano, Via Saldini 50, I-20133 Milano, Italy
Email: lourenco.beirao@unimi.it

Marco Verani
Affiliation: MOX, Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133 Milano, Italy
Email: marco.verani@polimi.it

DOI: http://dx.doi.org/10.1090/S0025-5718-2013-02670-1
Keywords: Mimetic Finite Difference Methods, obstacle problems
Received by editor(s): May 10, 2010
Received by editor(s) in revised form: April 26, 2011
Published electronically: February 20, 2013
Additional Notes: The first and the third authors were supported in part by the Italian research project PRIN 2008: “Analysis and development of advanced numerical methods for PDEs”.
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.