A posteriori error estimates and an adaptive scheme of least-squares meshfree method

A posteriori error estimates and an adaptive re nement scheme of rst-order least-squares meshfree method (LSMFM) are presented. The error indicators are readily computed from the residual. For an elliptic problem, the error indicators are further improved by applying the Aubin–Nitsche method. It is demonstrated, through numerical examples, that the error indicators coherently re ect the actual error. In the proposed re nement scheme, Voronoi cells are used for inserting new nodes at appropriate positions. Numerical examples show that the adaptive rst-order LSMFM, which combines the proposed error indicators and nodal re nement scheme, is e ectively applied to the localized problems such as the shock formation in uid dynamics