Quadrature for meshless methods

In this paper we discuss quadrature for meshless methods. We present results of two analyses. The first of these was developed in [1] and the second was developed in [2]. Using a simple example we show that a natural quadrature scheme that satisfies no special properties, leads to severe inaccuracies in the approximate solution. We then show in the first analysis that a simple correction to the stiffness matrix controls the effect of the quadrature. In the second analysis we show that if the quadrature scheme satisfies Green’s formula, then the effect of the quadrature is controlled.

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