An a posteriori error estimate for the generalized finite element method for transient heat diffusion problems

作者：Iqbal Muhammad; Gimperlein Heiko; Mohamed M Shadi^*; Laghrouche Omar

来源：International Journal for Numerical Methods in Engineering, 2017, 110(12): 1103-1118.

DOI：10.1002/nme.5440

• finite element methods
• error estimation
• thermal effects
• adaptivity
• extended finite element method
• generalized finite element method

We propose the study of a posteriori error estimates for time-dependent generalized finite element simulations of heat transfer problems. A residual estimate is shown to provide reliable and practically useful upper bounds for the numerical errors, independent of the heuristically chosen enrichment functions. Two sets of numerical experiments are presented. First, the error estimate is shown to capture the decrease in the error as the number of enrichment functions is increased or the time discretization refined. Second, the estimate is used to predict the behaviour of the error where no exact solution is available. It also reflects the errors incurred in the poorly conditioned systems typically encountered in generalized finite element methods. Finally, we study local error indicators in individual time steps and elements of the mesh. This creates a basis towards the adaptive selection and refinement of the enrichment functions.

• 出版日期2017-6-22