Recently the hp version of the finite element method has received increasing attention. This is an adaptive finite element approach in which adaptivity occurs in both the size, h, of the elements and in the order, p, of the approximating piecewise polynomials. The objective is to determine a distribution of h and p that minimizes the error using the least amount of work in some measure. It is desirable to combine this optimal order discretization method with an optimal order algebraic solution method, such as multigrid. An intriguing notion is to use the values of p as the levels of a multilevel method. In this paper we present such a method, known as hp-multigrid, for high order finite elements and hp-adaptive grids. Numerical results suggest the method has a convergence rate of 1/2 for Poisson's equation.
Citation: Numerical Linear Algebra With Applications
Pub Type: Journals
elliptic partial differential equations, finite elements, hp adaptive refinement, multigrid, p-multigrid