reproducing kernel particle method (RKPM); meshfree methods; goal-oriented error estimation; dual problem
Error-controlled adaptive meshfree methods are presented for both global error measures, such as the energy norm, and goal-oriented error measures in terms of quantities of interest. The meshfree method chosen in this paper is the reproducing kernel particle method (RKPM), since it is based on a Galerkin scheme and therefore allows extensions of quality control approaches as already developed for the finite element method. Our approach of goal-oriented error estimation is based on the well-established technique using an auxiliary dual problem. To keep the formulation general and to add versatility, a multi-space approach is used, where the dual problem is solved numerically using a different approximation space than the one employed in the associated primal problem. This can be realized with meshfree methods at no additional cost. Possible merits of this multi-space approach are discussed and an illustrative numerical example is presented.