A quasi-dual Lagrange multiplier space for serendipity mortar finite elements in 3D

Bishnu P. Lamichhane; Barbara I. Wohlmuth

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 38, Issue: 1, page 73-92
  • ISSN: 0764-583X

Abstract

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Domain decomposition techniques provide a flexible tool for the numerical approximation of partial differential equations. Here, we consider mortar techniques for quadratic finite elements in 3D with different Lagrange multiplier spaces. In particular, we focus on Lagrange multiplier spaces which yield optimal discretization schemes and a locally supported basis for the associated constrained mortar spaces in case of hexahedral triangulations. As a result, standard efficient iterative solvers as multigrid methods can be easily adapted to the nonconforming situation. We present the discretization errors in different norms for linear and quadratic mortar finite elements with different Lagrange multiplier spaces. Numerical results illustrate the performance of our approach.

How to cite

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Lamichhane, Bishnu P., and Wohlmuth, Barbara I.. "A quasi-dual Lagrange multiplier space for serendipity mortar finite elements in 3D." ESAIM: Mathematical Modelling and Numerical Analysis 38.1 (2010): 73-92. <http://eudml.org/doc/194209>.

@article{Lamichhane2010,
abstract = { Domain decomposition techniques provide a flexible tool for the numerical approximation of partial differential equations. Here, we consider mortar techniques for quadratic finite elements in 3D with different Lagrange multiplier spaces. In particular, we focus on Lagrange multiplier spaces which yield optimal discretization schemes and a locally supported basis for the associated constrained mortar spaces in case of hexahedral triangulations. As a result, standard efficient iterative solvers as multigrid methods can be easily adapted to the nonconforming situation. We present the discretization errors in different norms for linear and quadratic mortar finite elements with different Lagrange multiplier spaces. Numerical results illustrate the performance of our approach. },
author = {Lamichhane, Bishnu P., Wohlmuth, Barbara I.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Mortar finite elements; Lagrange multiplier; dual space; domain decomposition; nonmatching triangulation.; error bounds; domain decomposition; finite elements; hexahedral triangulations; multigrid methods; numerical results},
language = {eng},
month = {3},
number = {1},
pages = {73-92},
publisher = {EDP Sciences},
title = {A quasi-dual Lagrange multiplier space for serendipity mortar finite elements in 3D},
url = {http://eudml.org/doc/194209},
volume = {38},
year = {2010},
}

TY - JOUR
AU - Lamichhane, Bishnu P.
AU - Wohlmuth, Barbara I.
TI - A quasi-dual Lagrange multiplier space for serendipity mortar finite elements in 3D
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 38
IS - 1
SP - 73
EP - 92
AB - Domain decomposition techniques provide a flexible tool for the numerical approximation of partial differential equations. Here, we consider mortar techniques for quadratic finite elements in 3D with different Lagrange multiplier spaces. In particular, we focus on Lagrange multiplier spaces which yield optimal discretization schemes and a locally supported basis for the associated constrained mortar spaces in case of hexahedral triangulations. As a result, standard efficient iterative solvers as multigrid methods can be easily adapted to the nonconforming situation. We present the discretization errors in different norms for linear and quadratic mortar finite elements with different Lagrange multiplier spaces. Numerical results illustrate the performance of our approach.
LA - eng
KW - Mortar finite elements; Lagrange multiplier; dual space; domain decomposition; nonmatching triangulation.; error bounds; domain decomposition; finite elements; hexahedral triangulations; multigrid methods; numerical results
UR - http://eudml.org/doc/194209
ER -

References

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