Steve McCormick

First-order system least squares for second-order partial differential equations: part I

This paper develops a least-squares functional that arises from recasting general second-order uniformly elliptic partial differential equations in

The finite volume element method for diffusion equations on general triangulations

n=2

On the accuracy of the finite volume element method for diffusion equations on composite grids

or

An algebraic theory for multigrid methods for variational problems

3

A multilevel variational method for Au= Bu on composite Grids

dimensions as a system of first-order equations. In part I [Z. Cai, R. D. Lazarov, T. Manteuffel, and S. McCormick, SIAM J. Numer. Anal., 31 (1994), pp. 1785--1799] a similar functional was developed and shown to be elliptic in the

Multigrid Methods for Nearly Singular Linear Equations and Eigenvalue Problems

H(\divv) \times H^1

The finite volume-element method (FVE) for planar cavity flow

norm and to yield optimal convergence for finite element subspaces of

A Nonlinear Multigrid Solver for a Semi-Lagrangian Potential Vorticity-Based Shallow-Water Model on the Sphere

H(\divv) \times H^1

A finite volume convergence theory for the fast adaptive composite grid methods

. In this paper the functional is modified by adding a compatible constraint and imposing additional boundary conditions on the first-order system. The resulting functional is proved to be elliptic in the

Computational complexity of the fast adaptive composite grid (FAC) method

(H^1)^{n+1}