Local adaptive [formula omitted]-enrichments and generalized finite elements for transient heat diffusion problems

Abstract

A residual a-posteriori error estimate is used in conjunction with a q−adaptive procedure for selecting enrichment functions in the modelling of transient heat diffusion problems with the Generalized Finite Element Method (GFEM). The error estimate allows to assess local as well as global errors of the GFEM solutions and provides a tool to adaptively enrich the approximation space. With the proposed adaptive algorithm, the total number of degrees of freedom (DOFs) is significantly reduced in comparison to uniform enrichment. For a comparable accuracy, a reduction of up to 80% in DOFs is achieved. Moreover, the error estimate captures the deterioration of the conditioning of the system matrix typically encountered in enrichment based methods and enables the possibility of keeping the condition number within an acceptable limit.