High‐order multigrid strategies for hybrid high‐order discretizations of elliptic equations

Multigrid Algorithms for hp-Discontinuous Galerkin Discretizations of Elliptic Problems

We present W-cycle 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 multigrid analysis, we define a smoothing and an approximation property, which are used to prove the uniform convergence of the W-cycle scheme with respect to the gra...

Spectral Multigrid Methods for Elliptic Equations Ii

On the Construction of Discretizations of Elliptic Partial Differential Equations

Dedicated to Gerry Ladas on the occasion of his 60th Birthday Algorithmic aspects of a class of nite element collocation methods for the approximate numerical solution of elliptic partial diierential equations are described. Locally, for each nite element, the approximate solution is a polynomial. Polynomials corresponding to adjacent nite elements need not match continuously, but their values ...

A Multigrid Method for Nonlinear Unstructured Finite Element Elliptic Equations

This paper presents an application of the element agglomeration-based coarsening procedure (agglomeration AMGe) proposed in [10], to build the components of a multigrid method for solving nonlinear finite element elliptic equations on general unstructured meshes. The agglomeration-based AMGe offers the ability to define coarse elements and element matrices, provided access to elements and eleme...

Algebraic Multigrid for Discontinuous Galerkin Discretizations

We present a new algebraic multigrid (AMG) algorithm for the solution of linear systems arising from discontinuous Galerkin discretizations of heterogeneous elliptic problems. The algorithm is based on the idea of subspace corrections and the first coarse level space is the subspace spanned by continuous linear basis functions. The linear system associated with this space is constructed algebra...