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 (GFEMgl) to problems of transient heat transfer involving localized features. The GFEMgl 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 GFEMgl 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.