Efficient numerical solution of mixed finite element discretizations by adaptive multilevel methods

Ronald H.W. Hoppe; Barbara Wohlmuth

Applications of Mathematics (1995)

  • Volume: 40, Issue: 3, page 227-248
  • ISSN: 0862-7940

Abstract

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We consider mixed finite element discretizations of second order elliptic boundary value problems. Emphasis is on the efficient iterative solution by multilevel techniques with respect to an adaptively generated hierarchy of nonuniform triangulations. In particular, we present two multilevel solvers, the first one relying on ideas from domain decomposition and the second one resulting from mixed hybridization. Local refinement of the underlying triangulations is done by efficient and reliable a posteriori error estimators which can be derived by a defect correction in higher order ansatz spaces or by taking advantage of superconvergence results. The performance of the algorithms is illustrated by several numerical examples.

How to cite

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Hoppe, Ronald H.W., and Wohlmuth, Barbara. "Efficient numerical solution of mixed finite element discretizations by adaptive multilevel methods." Applications of Mathematics 40.3 (1995): 227-248. <http://eudml.org/doc/32917>.

@article{Hoppe1995,
abstract = {We consider mixed finite element discretizations of second order elliptic boundary value problems. Emphasis is on the efficient iterative solution by multilevel techniques with respect to an adaptively generated hierarchy of nonuniform triangulations. In particular, we present two multilevel solvers, the first one relying on ideas from domain decomposition and the second one resulting from mixed hybridization. Local refinement of the underlying triangulations is done by efficient and reliable a posteriori error estimators which can be derived by a defect correction in higher order ansatz spaces or by taking advantage of superconvergence results. The performance of the algorithms is illustrated by several numerical examples.},
author = {Hoppe, Ronald H.W., Wohlmuth, Barbara},
journal = {Applications of Mathematics},
keywords = {elliptic boundary value problems; mixed finite element methods; adaptive multilevel techniques; mixed finite element; second-order elliptic boundary value problems; nonuniform triangulations; domain decomposition; multilevel preconditioned conjugate gradient iteration; adaptive multilevel method; local refinement; error estimators; defect correction; superconvergence; performance; test examples; boundary layers},
language = {eng},
number = {3},
pages = {227-248},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Efficient numerical solution of mixed finite element discretizations by adaptive multilevel methods},
url = {http://eudml.org/doc/32917},
volume = {40},
year = {1995},
}

TY - JOUR
AU - Hoppe, Ronald H.W.
AU - Wohlmuth, Barbara
TI - Efficient numerical solution of mixed finite element discretizations by adaptive multilevel methods
JO - Applications of Mathematics
PY - 1995
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 40
IS - 3
SP - 227
EP - 248
AB - We consider mixed finite element discretizations of second order elliptic boundary value problems. Emphasis is on the efficient iterative solution by multilevel techniques with respect to an adaptively generated hierarchy of nonuniform triangulations. In particular, we present two multilevel solvers, the first one relying on ideas from domain decomposition and the second one resulting from mixed hybridization. Local refinement of the underlying triangulations is done by efficient and reliable a posteriori error estimators which can be derived by a defect correction in higher order ansatz spaces or by taking advantage of superconvergence results. The performance of the algorithms is illustrated by several numerical examples.
LA - eng
KW - elliptic boundary value problems; mixed finite element methods; adaptive multilevel techniques; mixed finite element; second-order elliptic boundary value problems; nonuniform triangulations; domain decomposition; multilevel preconditioned conjugate gradient iteration; adaptive multilevel method; local refinement; error estimators; defect correction; superconvergence; performance; test examples; boundary layers
UR - http://eudml.org/doc/32917
ER -

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