A comparison study on different MLPG(LBIE) formulations
V. Vavourakis; E. J. Sellountos; and D. Polyzos

Source CMES: Computer Modeling in Engineering & Sciences, Vol. 13, No. 3, pp. 171-184, 2006
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Keywords Meshless Local Petrov-Galerkin method, MLPG, Local Boundary Integral Equation method, LBIE, MLS, RBPIF, elasticity.
Abstract Comparison studies on the accuracy provided by five different elastostatic Meshless Local Petrov-Galerkin (MLPG) type formulations, based on Local Boundary Integral Equation (LBIE) considerations, are made. The main differences of these MLPG(LBIE) formulations, as they compared to each other, are concentrated on the treatment of tractions on the local and global boundaries and the way of imposing the boundary conditions of the elastostatic problem. Both the Moving Least Square (MLS) approximation scheme and the Radial Basis Point Interpolation Functions (RBPIF) are exploited for the interpolation of the interior and boundary variables. Two representative elastostatic problems are solved and the relative error$L_2$ norms of displacements obtained by the aforementioned MLPG(LBIE)/MLS and MLPG(LBIE)/RBPIF formulations are evaluated for regular and irregular distributions of nodal points, as well as for different support domain radii. Useful conclusions on the accuracy and the stability of a MLPG(LBIE) method are addressed.
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