Adaptive Mesh Refinement for the Time-Dependent Nodal Integral Method

Adaptive mesh refinement capability has been developed and implemented for the time-dependent nodal integral method (NIM). The combination of adaptive mesh refinement (AMR) with the NIM maintains the coarse mesh efficiency of the nodal method by allowing high resolution only in regions where it is needed. Furthermore, exploiting certain features of the nodal method, such as using transverse-integrated variables for efficient error estimation and using node interior reconstruction to develop accurate interpolation operators, can enhance the AMR process. In this work, the NIM-AMR is formally developed, and applications of the NIM-AMR to convection-diffusion problems are presented. Results show that for a given accuracy, the NIM-AMR can be several times faster than the NIM alone.