A meshfree weak-strong form method

Abstract

A novel meshfree weak-strong (MWS) form method is proposed based on a combined formulation of both the local weak form and the strong form. In the MWS method, the problem domain and its boundary is represented by a set of distributed nodes. The strong form or the collocation method is used for all internal nodes and the nodes on the essential boundaries. The local weak form (Petrov-Galerkin weak form) is used for nodes on or near the natural boundaries. The natural boundary conditions can then be easily imposed to produce stable and accurate solutions. The MWS method has advantages of both meshfree methods based on strong forms and weak forms. In the entire problem, only local integration "meshes" for nodes on or near the natural boundary are required.