A moving least square reproducing polynomial meshless method

doi:10.1016/j.apnum.2013.03.001

Applied Numerical Mathematics

Volume 69, July 2013, Pages 34-58

https://doi.org/10.1016/j.apnum.2013.03.001 Get rights and content

Abstract

Interest in meshless methods has grown rapidly in recent years in solving boundary value problems (BVPs) arising in science and engineering. In this paper, we present the moving least square radial reproducing polynomial (MLSRRP) meshless method as a generalization of the moving least square reproducing kernel particle method (MLSRKPM). The proposed method is established upon the extension of the MLSRKPM basis by using the radial basis functions. Some important properties of the shape functions are discussed. An interpolation error estimate is given to assess the convergence rate of the approximation. Also, for some class of time-dependent partial differential equations, the error estimate is acquired. The efficiency of the present method is examined by several test problems. The studied method is applied to the parabolic two-dimensional transient heat conduction equation and the hyperbolic two-dimensional sine-Gordon equation which are discretized by the aid of the meshless local Petrov–Galerkin (MLPG) method.

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A moving least square reproducing polynomial meshless method

Abstract

Comput. Methods Appl. Mech. Engrg.

Comput. Methods Appl. Mech. Engrg.

J. Comput. Appl. Math.

Physica D

Math. Comput. Simulation

Comput. Phys. Comm.

Math. Comput. Simulation

J. Comput. Appl. Math.

Comput. Methods Appl. Mech. Engrg.

Comput. Math. Appl.

Comput. Methods Appl. Mech. Engrg.

Comput. Methods Appl. Mech. Engrg.

J. Comput. Appl. Math.

Math. Comput. Simulation

Int. J. Non-Linear Mech.

Eng. Anal. Bound. Elem.

Eng. Anal. Bound. Elem.

Appl. Math. Model.

The Meshless Method (MLPG) for Domain and BIE Discretizations

The meshless local Petrov–Galerkin (MLPG) method: a simple and less-costly alternative to the finite element and boundary element methods

CMES Comput. Model. Eng. Sci.

The Meshless Local Petrov–Galerkin (MLPG) Method

A new meshless local Petrov–Galerkin (MLPG) approach in computational mechanics

Comput. Mech.

Element-free Galerkin methods

Internat. J. Numer. Methods Engrg.

An explicit numerical scheme for the sine-Gordon equation in 2+1 dimensions

Appl. Numer. Anal. Comput. Math.

A modified predictor–corrector scheme for the two-dimensional sine-Gordon equation

Numer. Algorithms

Recent developments in stabilized Galerkin and collocation meshfree method

Comput. Assist. Mech. Eng. Sci.

Reproducing kernel enhanced local radial basis collocation method

Internat. J. Numer. Methods Engrg.

An explicit numerical scheme for the sine-Gordon equation in $2 + 1$ dimensions