Nodal partition of explicit finite element methods for unsteady diffusion problems

Abstract A variable explicit finite element method is presented for solving unsteady diffusion problems in one or more space dimensions. For numerical time integration, the computational mesh is partitioned into as many parts as the number of nodes. The time increment appropriate to each node is automatically determined according to a nodal stability criterion applicable to arbitrary element meshes. Numerical examples based on bilinear and biquadratic elements are included to illustrate the efficiency and accuracy of the proposed method.