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This paper develops ellipticity estimates and discretization error bounds for elliptic equations (with lower order terms) that are reformulated as a least{squares problem for an equivalent rst{orderâ€¦ (More)

- Marian Brezina, Andrew J. Cleary, +5 authors John W. Ruge
- SIAM J. Scientific Computing
- 2001

We introduce AMGe, an algebraic multigrid method for solving the discrete equations that arise in Ritz-type finite element methods for partial differential equations. Assuming access to the elementâ€¦ (More)

This paper develops a least-squares functional that arises from recasting general second-order uniformly elliptic partial differential equations in n = 2 or 3 dimensions as a system of first-orderâ€¦ (More)

Following our earlier work on general second-order scalar equations, here we develop a least-squares functional for the twoand three-dimensional Stokes equations, generalized slightly by allowing aâ€¦ (More)

This paper develops two first-order system least-squares (FOSLS) approaches for the solution of the pure traction problem in planar linear elasticity. Both are two-stage algorithms that first solveâ€¦ (More)

- Hans De Sterck, Thomas A. Manteuffel, +4 authors Geoffrey Sanders
- SIAM J. Scientific Computing
- 2010

A smoothed aggregation multigrid method is presented for the numerical calculation of the stationary probability vector of an irreducible sparse Markov chain. It is shown how smoothing theâ€¦ (More)

- Hans De Sterck, Thomas A. Manteuffel, Stephen F. McCormick, Quoc Nguyen, John W. Ruge
- SIAM J. Scientific Computing
- 2008

A multilevel adaptive aggregation method for calculating the stationary probability vector of an irreducible stochastic matrix is described. The method is a special case of the adaptive smoothedâ€¦ (More)

This paper develops a least-squares approach to the solution of the incompressible Navierâ€“Stokes equations in primitive variables. As with our earlier work on Stokes equations, we recast theâ€¦ (More)

- James J. Brannick, Marian Brezina, Scott P. MacLachlan, Thomas A. Manteuffel, Stephen F. McCormick, John W. Ruge
- Numerical Lin. Alg. with Applic.
- 2006

Algebraic multigrid (AMG) is an iterative method that is often optimal for solving the matrix equations that arise in a wide variety of applications, including discretized partial differentialâ€¦ (More)

We establish an a-posteriori error estimate, with corresponding bounds, that is valid for any FOSLS L2-minimization problem. Such estimates follow almost immediately from the FOSLS formulation, butâ€¦ (More)