Transient analysis of sharp thermal gradients using coarse finite element meshes

This paper investigates the application of the generalized finite element method with global-local enrichments (GFEM^gl) to problems of transient heat transfer involving localized features. The GFEM^gl is utilized in order to numerically construct general, specially-tailored shape functions yielding high levels of accuracy on coarse FEM meshes. The use of time-dependent shape functions requires that the system of equations be discretized temporally first, and then spatially in order to properly account for the time-dependency. The standard α-method is used for the time integration scheme. The transient three-dimensional GFEM^gl is then applied to a laser heating example in order to demonstrate its ability to resolve localized, transient features on a fixed, coarse mesh. Convergence analysis of the proposed method as well as applications to heterogeneous materials, and moving heat sources are also provided.