Uniform Convergence of Multigrid V-Cycle on Adaptively Refined Finite Element Meshes for Elliptic Problems with Discontinuous Coefficients (Communications in Mathematical Research, 2023)
The multigrid V-cycle methods for adaptive finite element discretizations of two-dimensional elliptic problems with discontinuous coefficients areconsidered. Under the conditions that the coefficient is quasi-monotone up toa constant and the meshes are locally refined by using the newest vertex bisection algorithm, some uniform convergence results are proved for the standardmultigrid V-cycle algorithm with Gauss-Seidel relaxations performed only onnew nodes and their immediate neighbours. The multigrid V-cycle algorithmuses $\mathcal{O}(N)$ operations per iteration and is optimal.