MULTIGRID ALGORITHMS FOR hp-DISCONTINUOUS GALERKIN DISCRETIZATIONS OF ELLIPTIC PROBLEMS

作者：Antonietti Paola F^*; Sarti Marco; Verani Marco

来源：SIAM Journal on Numerical Analysis, 2015, 53(1): 598-618.

DOI：10.1137/130947015

• hp-version discontinuous Galerkin
• multigrid algorithms
• elliptic problems
• geometric multigrid

We present W-cycle h-, p-, and hp-multigrid algorithms for the solution of the linear system of equations arising from a wide class of hp-version discontinuous Galerkin discretizations of elliptic problems. Starting from a classical framework in geometric multigrid analysis, we define a smoothing and an approximation property, which are used to prove uniform convergence of the W-cycle scheme with respect to the discretization parameters and the number of levels, provided the number of smoothing steps is chosen of order p(2+mu), where p is the polynomial approximation degree and mu = 0, 1. A discussion on the effects of employing inherited or noninherited sublevel solvers is also presented. Numerical experiments confirm the theoretical results.

• 出版日期2015