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A coupled finite element and meshless local Petrov–Galerkin method for two-dimensional potential problems.(English)Zbl 1037.65115

Summary: A coupled finite element (FE) and meshless local Petrov-Galerkin (MLPG) method for analyzing two-dimensional potential problems is presented. A transition region is created between the FE and MLPG regions. The transition region blends the trial and test functions of the FE and MLPG regions. The trial function blending is achieved using a new coupling technique similar to the ‘Coons’ patch method that is widely used in computer aided geometric design.
By using the technique, trial functions, which are similar to the isoparametric “serendipity” element, of the transition element can be constructed. The test function blending is achieved by using either the FE or MLPG test functions on the nodes. Several potential problems are used to establish the validity of the coupled method.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation

Cite

References:

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This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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