A posteriori error estimator and indicator in generalized finite differences. Application to improve the approximated solution of elliptic PDEs

Abstract

In this paper we compare two different procedures of approximation of the a posteriori error for the GFD method; both procedures are residual based errors. The performance of the two different approximations of the error is illustrated by analysing different second order partial differential equations in 2D problems with known analytical solutions, using an irregular cloud of points. Also, in this paper an adaptive method for improving solutions using a posteriori error is shown.

Keywords:

• Adaptive method
• A posteriori error approximation
• Generalized finite differences
• Meshless methods