Thomas A. Manteuffel

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 Tchebychev iteration for nonsymmetric linear systems

n=2

Necessary and Sufficient Conditions for the Existence of a Conjugate Gradient Method

or

A taxonomy for conjugate gradient methods

3

The numerical solution of second-order boundary value problems on nonuniform meshes

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

First-Order System Least Squares for the Stokes Equations, with Application to Linear Elasticity

H(\divv) \times H^1

Robustness and Scalability of Algebraic Multigrid

norm and to yield optimal convergence for finite element subspaces of

Adaptive procedure for estimating parameters for the nonsymmetric Tchebychev iteration

H(\divv) \times H^1

Supra-convergent schemes on irregular grids

. 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

Analysis of Velocity-Flux First-Order System Least-Squares Principles for the Navier--Stokes Equations: Part I

(H^1)^{n+1}