The influence of quadrature formula in 2D and 3D mortar methods

Niveau: Secondaire, Lycée, Terminale
The in uen e of quadrature formulas in 2D and 3D mortar element methods Yvon Maday 1 , Fran es a Rapetti 1 , and Barbara I. Wohlmuth 2 1 Laboratoire d'Analyse Numerique, Paris 6 University, Bo^te ourrier 187, 75252 Paris edex 05, Fran e 2 Mathematis hes Institut A, Universitat Stuttgart, Pfaenwaldring 57, 70 569 Stuttgart, Germany Abstra t. The paper is on erned with the mortar nite element dis retization of s alar ellipti equations in three dimensions. The attention is fo used on the in uen e of quadrature formulas on the dis retization error. We show numeri ally that the optimality of the method is preserved if suitable quadrature formulas are used. 1 Introdu tion The mortar element method, rstly proposed in [3?, is a non- onforming non- overlapping domain de omposition method. The oupling of dierent phys- i al models, dis retization s hemes or non-mat hing triangulations at the interfa es an be eÆ iently realized in terms of mortar element methods. To preserve the global optimality of the lo ally adapted dis retizations, the in- terfa es between the dierent regions have to be handled appropriately. Due to its high exibility, this approa h has been analysed and implemented in many situations.

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