The dimension split element-free Galerkin method for three-dimensional potential problems. (English) Zbl 1404.65275
Summary: This paper presents the dimension split element-free Galerkin (DSEFG) method for three-dimensional potential problems, and the corresponding formulae are obtained. The main idea of the DSEFG method is that a three-dimensional potential problem can be transformed into a series of two-dimensional problems. For these two-dimensional problems, the improved moving least-squares (IMLS) approximation is applied to construct the shape function, which uses an orthogonal function system with a weight function as the basis functions. The Galerkin weak form is applied to obtain a discretized system equation, and the penalty method is employed to impose the essential boundary condition. The finite difference method is selected in the splitting direction. For the purposes of demonstration, some selected numerical examples are solved using the DSEFG method. The convergence study and error analysis of the DSEFG method are presented. The numerical examples show that the DSEFG method has greater computational precision and computational efficiency than the IEFG method.
MSC:
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65N06 | Finite difference methods for boundary value problems involving PDEs |
Keywords:
dimension split method; improved moving least-squares (IMLS) approximation; improved element-free Galerkin (IEFG) method; finite difference method (FDM); dimension split element-free Galerkin (DSEFG) method; potential problemReferences:
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