2011
DOI: 10.1007/s00466-011-0613-6
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The finite point method for the p-Laplace equation

Abstract: In this paper, the finite point method (FPM) is presented for solving the 2D, nonlinear, elliptic p-Laplace or p-harmonic equation. The FPM is a truly meshfree technique based on the combination of the moving least squares approximation on a cloud of points with the point collocation method to discretize the governing equation. The lack of dependence on a mesh or integration procedure is an important feature, which makes the FPM simple, efficient and applicable to solve nonlinear problems. Applications are dem… Show more

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Cited by 18 publications
(3 citation statements)
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“…The strong‐form meshfree methods possess the following attractive advantages. They are truly meshfree and the implementing procedure is straightforward . The proposed method is a meshfree point collocation method that the governing equations, the boundary conditions and the jump conditions are discretized by the collocation technique.…”
Section: Methodsmentioning
confidence: 99%
“…The strong‐form meshfree methods possess the following attractive advantages. They are truly meshfree and the implementing procedure is straightforward . The proposed method is a meshfree point collocation method that the governing equations, the boundary conditions and the jump conditions are discretized by the collocation technique.…”
Section: Methodsmentioning
confidence: 99%
“…Meshfree method has attracted attention in mechanics and practical engineering, and been widely used in the study of the THCP. At present, many meshfree methods have been developed, such as smooth particle hydrodymics (Abbreviation: SPH, proposed by Lucyt and Gingold in 1977) [18,19], element-free Galerkin method (Abbreviation: EFGM, proposed by Belytschko in 1994) [20][21][22], meshfree local Petrov-Galerkin method (Abbreviation: MLPG, proposed by Atluri in 1998) [23][24][25][26], reproducing kernel particle method (Abbreviation: RKPM, proposed by Liu in 2005) [27][28][29][30], radial basis functions method (Abbreviation: RBF, proposed by Žilinskas in 2010) [31,32], complex variable meshfree manifold method (Abbreviation: CVMMM, proposed by Gao in 2010) [33], the finite point method (Abbreviation: FPM, proposed by Tatari in 2011) [34,35], Hermit-type reproducing kernel particle method (Abbreviation: Hermit-type RKPM, proposed by Ma in 2017) [36][37][38][39] and boundary integral equation method (Abbreviation: BIE, proposed by Mantegh in 2010) [40,41], etc.…”
Section: Introductionmentioning
confidence: 99%
“…There are a variety of meshless methods, such as the reproducing kernel particle method (RKPM), [5][6][7][8] discontinuous Galerkin method (DGM), [9] polynomial point interpolation method (PPIM), [10,11] boundary integral equation method (BIEM), [12,13] element-free Galerkin method (EFGM), [14][15][16][17] moving least-squares method (MLSM), [18][19][20] smooth parti-cle hydrodynamics (SPH), [21,22] iterative Galerkin method (IGM), [23] radial basis function method (RBFM), [24,25] the partition of unity method (PUM), [26,27] meshless local Petrov-Galerkin method (MLPG), [28][29][30][31] finite point method (FPM), [32,33] Hermite-type radial point interpolation method (Hermite-type RPIM), [34][35][36] meshless manifold method (MMM), [37,38] and complex variable meshless method (CVMM). [39,40] The SPH method, which is based on the kernel estimate introduced by Monaghan, is the earliest meshless method.…”
Section: Introductionmentioning
confidence: 99%