Volume 52, Number 1, January–February 2018
|Page(s)||337 - 364|
|Published online||28 May 2018|
A multigrid algorithm for the p-version of the virtual element method
MOX, Dipartimento di Matematics, Politecnico di Milano,
2 Faculty of Mathematics, University of Vienna, 1090 Vienna, Austria
* Corresponding author: email@example.com
Accepted: 11 November 2018
We present a multigrid algorithm for the solution of the linear systems of equations stemming from the p-version of the virtual element discretization of a two-dimensional Poisson problem. The sequence of coarse spaces are constructed decreasing progressively the polynomial approximation degree of the virtual element space, as in standard p-multigrid schemes. The construction of the interspace operators relies on auxiliary virtual element spaces, where it is possible to compute higher order polynomial projectors. We prove that the multigrid scheme is uniformly convergent, provided the number of smoothing steps is chosen sufficiently large. We also demonstrate that the resulting scheme provides a uniform preconditioner with respect to the number of degrees of freedom that can be employed to accelerate the convergence of classical Krylov-based iterative schemes. Numerical experiments validate the theoretical results.
Mathematics Subject Classification: 65N30 / 65N55
Key words: Polygonal meshes / virtual element methods / p Galerkin methods / p multigrid
© EDP Sciences, SMAI 2018
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