Mixed methods for degenerate elliptic problems and application to fractional Laplacian

We analyze the approximation by mixed finite element methods of solutions of equations of the form −div (a ∇u) = g , where the coefficient a  = a (x ) can degenerate going to zero or infinity. First, we extend the classic error analysis to this case provided that the coefficient a belongs to the Muc...

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Autores principales: Cejas, María Eugenia, Durán, Ricardo Guillermo, Prieto, Mariana I.
Formato: Articulo
Lenguaje:Inglés
Publicado: 2021
Materias:
Matemática
Mixed finite elements
Degenerate elliptic problems
Fractional Laplacian
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/124331
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-124331
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Matemática
Mixed finite elements
Degenerate elliptic problems
Fractional Laplacian
spellingShingle Matemática
Mixed finite elements
Degenerate elliptic problems
Fractional Laplacian
Cejas, María Eugenia
Durán, Ricardo Guillermo
Prieto, Mariana I.
Mixed methods for degenerate elliptic problems and application to fractional Laplacian
topic_facet Matemática
Mixed finite elements
Degenerate elliptic problems
Fractional Laplacian
description We analyze the approximation by mixed finite element methods of solutions of equations of the form −div (a ∇u) = g , where the coefficient a  = a (x ) can degenerate going to zero or infinity. First, we extend the classic error analysis to this case provided that the coefficient a belongs to the Muckenhoupt class A 2 . The analysis developed applies to general mixed finite element spaces satisfying the standard commutative diagram property, whenever some stability and interpolation error estimates are valid in weighted norms. Next, we consider in detail the case of Raviart–Thomas spaces of arbitrary order, obtaining optimal order error estimates for simplicial elements in any dimension and for convex quadrilateral elements in the two dimensional case, in both cases under a regularity assumption on the family of meshes. For the lowest order case we show that the regularity assumption can be removed and prove anisotropic error estimates which are of interest in problems with boundary layers. Finally we apply the results to a problem arising in the solution of the fractional Laplace equation.
format Articulo
Articulo
author Cejas, María Eugenia
Durán, Ricardo Guillermo
Prieto, Mariana I.
author_facet Cejas, María Eugenia
Durán, Ricardo Guillermo
Prieto, Mariana I.
author_sort Cejas, María Eugenia
title Mixed methods for degenerate elliptic problems and application to fractional Laplacian
title_short Mixed methods for degenerate elliptic problems and application to fractional Laplacian
title_full Mixed methods for degenerate elliptic problems and application to fractional Laplacian
title_fullStr Mixed methods for degenerate elliptic problems and application to fractional Laplacian
title_full_unstemmed Mixed methods for degenerate elliptic problems and application to fractional Laplacian
title_sort mixed methods for degenerate elliptic problems and application to fractional laplacian
publishDate 2021
url http://sedici.unlp.edu.ar/handle/10915/124331
work_keys_str_mv AT cejasmariaeugenia mixedmethodsfordegenerateellipticproblemsandapplicationtofractionallaplacian
AT duranricardoguillermo mixedmethodsfordegenerateellipticproblemsandapplicationtofractionallaplacian
AT prietomarianai mixedmethodsfordegenerateellipticproblemsandapplicationtofractionallaplacian
bdutipo_str Repositorios
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