Some Weighted Averaging Methods for Gradient Recovery (Advances in Applied Mathematics and Mechanics, 2018)
We propose some new weighted averaging methods for gradient recovery,and present analytical and numerical investigation on the performance of theseweighted averaging methods. It is shown analytically that the harmonic averagingyields a superconvergent gradient for any mesh in one-dimension and the rectangularmesh in two-dimension. Numerical results indicate that these new weightedaveraging methods are better recovered gradient approaches than the simple averagingand geometry averaging methods under triangular mesh.