Open Access

ARTICLE

Application of the Generalized Finite Difference Method to improve the approximated solution of pdes

by J.J. Benito¹, F. Ure ˇna², L. Gavete³, B. Alonso³

1 UNED, Madrid, SPAIN.
2 UCLM, CR, Castilla-La Mancha, SPAIN.
3 UPM, Madrid, SPAIN.

Computer Modeling in Engineering & Sciences 2008, 38(1), 39-58. https://doi.org/10.3970/cmes.2008.038.039

Abstract

One of the most universal and effective methods, in wide use today, for solving equations of mathematical physics approximately is the finite difference method (FDM). The Generalized finite difference method (GFDM) is evolved fron classical (FDM), which can be applied over general or irregular clouds of points.
This paper starts by showing the GFDM. In this paper, this meshless method is used for solving second-order partial (pde's) with constant coefficients in any type of domain. The method gives the values of derivatives in the nodes using the direct application of the formulae in differences obtained.
The following points describe an a posteriori error estimator. This serves as a starting point for an h-adaptive method to improve the solution of pde's by selectively adding nodes to the domain.

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