Free mesh method: A new meshless finite element method

A new meshless finite element method, named as the Free Mesh Method, is proposed in this paper. Once nodes are arranged in the domain to be analyzed, some temporary triangular elements are set around a node, i.e. a current central node. The contributions from the element matrices of the above temporary elements are assembled to the total stiffness matrix. The above processes are performed on all the nodes in the domain. Finally, the solution is obtained by solving the total stiffness equation system as the usual finite element method. To demonstrate the effectiveness of the method, a simple two-dimensional heat conduction problem is solved.