Super-Convergence of the Symmetric Poisson Solver with Adaptive Grid Configuration

We review the super-convergence analyses in [1, 2] for the symmetric Poisson solver, introduced by Losasso et al. [3, 4], with adaptive grid configuration in the cases of regular and irregular domains. The symmetric Poisson solver is known to be second-order accurate and the order of its numerical gradient is emperically observed to be one and a half, which is called super-convergence, in [3, 4]. In this article, we provide the theoretical results from rigorous analyses on super-convergence property of the Poisson solver in [1, 2] and numerical results to support the theoretical results.