# A finite element method on composite grids based on Nitsche’s method

Anita Hansbo; Peter Hansbo; Mats G. Larson

- Volume: 37, Issue: 3, page 495-514
- ISSN: 0764-583X

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topHansbo, Anita, Hansbo, Peter, and Larson, Mats G.. "A finite element method on composite grids based on Nitsche’s method." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 37.3 (2003): 495-514. <http://eudml.org/doc/245706>.

@article{Hansbo2003,

abstract = {In this paper we propose a finite element method for the approximation of second order elliptic problems on composite grids. The method is based on continuous piecewise polynomial approximation on each grid and weak enforcement of the proper continuity at an artificial interface defined by edges (or faces) of one the grids. We prove optimal order a priori and energy type a posteriori error estimates in 2 and 3 space dimensions, and present some numerical examples.},

author = {Hansbo, Anita, Hansbo, Peter, Larson, Mats G.},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {Nitsche’s method; overlapping grids; finite element method; penality method; Poisson equation},

language = {eng},

number = {3},

pages = {495-514},

publisher = {EDP-Sciences},

title = {A finite element method on composite grids based on Nitsche’s method},

url = {http://eudml.org/doc/245706},

volume = {37},

year = {2003},

}

TY - JOUR

AU - Hansbo, Anita

AU - Hansbo, Peter

AU - Larson, Mats G.

TI - A finite element method on composite grids based on Nitsche’s method

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2003

PB - EDP-Sciences

VL - 37

IS - 3

SP - 495

EP - 514

AB - In this paper we propose a finite element method for the approximation of second order elliptic problems on composite grids. The method is based on continuous piecewise polynomial approximation on each grid and weak enforcement of the proper continuity at an artificial interface defined by edges (or faces) of one the grids. We prove optimal order a priori and energy type a posteriori error estimates in 2 and 3 space dimensions, and present some numerical examples.

LA - eng

KW - Nitsche’s method; overlapping grids; finite element method; penality method; Poisson equation

UR - http://eudml.org/doc/245706

ER -

## References

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- [10] R.D. Lazarov, J.E. Pasciak, J. Schöberl and P.S. Vassilevski, Almost optimal interior penalty discontinuous approximations of symmetric elliptic problems on non-matching grids. Technical Report, ISC-01-05-MATH (2001). Zbl1095.65103
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- [12] J. Nitsche, Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. Abh. Math. Sem. Univ. Hamburg 36 (1971) 9–15. Zbl0229.65079
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