Introductory

First-order system least squares philosophy, manuscript by the FOSLS gang.to provide basic understanding and encourage discussion.

1993

Multilevel first-order system least squares (FOSLS) for Helmholtz equations, S. McCormick, Procs. Conf. Maxwell Equations, D.C., John Wiley and Sons (1993).

1994

First-order system least squares for second-order partial differential equations: part I, Z. Cai, R. Lazarov, T. Manteuffel, and S. McCormick, SIAM J. Num. Anal. 31 (1994), pp. 1785-1802.

1997

First-order system least squares for second-order partial differential equations: part II, Z. Cai, T. Manteuffel, and S. McCormick, SIAM J. Num. Anal. 34 (1997), pp. 425-454.

First-order system least squares for the Stokes equations, with application to linear elasticity, Z. Cai, T. Manteuffel, and S. McCormick, SIAM J. Numer. Anal. 34 (1997), pp. 1727-1741.

First-order system least squares for the vorticity form of the Stokes equations, with application to linear elasticity, Z. Cai, T. Manteuffel, and S. McCormick, E.T.N.A. 3 (1997), pp. 150-159.

1998

Analysis of velocity-flux first-order system least-squares principles for the Navier-Stokes equations: Part I, P. Bochev, Z. Cai, T. Manteuffel, and S. McCormick, SIAM J. Numer. Anal. 35 (1998), pp. 990-1009.

First-order system least squares (FOSLS) for convection-diffusion problems: numerical results, J.-M. Fiard, T. Manteuffel, and S. McCormick, SIAM J. Sci. Comp. 19 (1998), pp. 1958-1979.

First-order system least squares for the pure traction problem in planar linear elasticity, Z. Cai, T. Manteuffel, S. McCormick, and S. Parter, SIAM J. Numer. Anal. 35 (1998), pp. 320-335.

Least-squares finite-element solution of the neutron transport equation in diffusive regimes, T. Manteuffel and K. Ressel, SIAM J. Num. Anal. 85 (1998), pp. 806-835.

Local error estimates and adaptive refinement for first-order system least squares (FOSLS), M. Berndt, T. Manteuffel, and S. McCormick, E.T.N.A. 6 (1998), pp. 35-43.

1999

Analysis of velocity-flux least-squares principles for the Navier-Stokes equations: Part II, P. Bochev, Z. Cai, T. Manteuffel, and S. McCormick, SIAM J. Numer. Anal. 36 (1999), pp. 1125-1144.

2000

First-order system least squares (FOSLS) for the Helmholtz equation, B. Lee, T. Manteuffel, S. McCormick, and J. Ruge, SIAM J. Sci. Comp. 21 (2000), pp. 1927-1949.

First-order system least squares for planar linear elasticity: numerical results, Z. Cai, C.-O. Lee, T. Manteuffel, and S. McCormick, SIAM J. Sci. Comp. 21 (2000), pp. 1706-1727.

First-order system least squares for the Stokes and elasticity equations: further results, Z. Cai, C.-O. Lee, T. Manteuffel, and S. McCormick, SIAM J. Sci. Comp. 21 (2000), pp. 1728-1739.

2001

First-order system least squares (FOSLS) for spatial linear elasticity: pure traction, S.-D. Kim, T. Manteuffel, and S. McCormick, SIAM J. Num. Anal. 38 (2001), pp. 1454-1482.

First-order system LL* (FOSLL*): scalar elliptic partial differential equations, Z. Cai, T. Manteuffel, and S. McCormick, SIAM J. Num. Anal. 39 (2001), pp. 1418-1445.

2002

First-order system least squares for elastohydrodynamics with application to flow in compliant blood vessels, J. J. Heys, C. G. DeGroff, W. W. Orlando, T. Manteuffel, and S. McCormick, Biomed. Sci. Instr. 38 (2002), pp. 277-282.

2003

Improved discretization error estimates for first- order system least squares (FOSLS), T. Manteuffel, S. McCormick, and C. Pflaum, J. Num. Math. 11 (2003), pp.163-177.

Multilevel first-order system least squares for elliptic grid generation, A. Codd, T. Manteuffel, S. McCormick, and J. Ruge, SIAM J. Numer. Anal. 41 (2003), pp. 2210-2232.

Multilevel first-order system least squares for nonlinear partial differential equations, A. Codd, T. Manteuffel, and S. McCormick, SIAM J. Numer. Anal. 41 (2003), pp. 2197-2209.

2004

A robust approach to minimizing H(div) dominated functionals in an H1-conforming finite element space, T. Austin, T. Manteuffel, and S. McCormick, J. Numer. Lin. Alg. Appl. 11 (2004), pp. 115-140.

First-order system least squares and electrical impedance tomography, H. MacMillan, S. McCormick, and T. Manteuffel, SIAM J. Numer. Anal. 42 (2004), pp. 461-483

First-order system least squares and electrical impedance tomography: part II, H. MacMillan, S. McCormick, and T. Manteuffel, manuscript (2004).

First-order system least squares for coupled fluid-elasticity problems, J. J. Heys, T. Manteuffel, S. McCormick, and J. Ruge, J. Comp. Phys. 195 (2004), pp. 560-575.

Least-squares finite element methods and algebraic multigrid solvers for linear hyperbolic PDEs, H. de Sterck, T. Manteuffel, S. McCormick, and L. Olson, SIAM J. Sci Comp. 26 (2004), pp. 31-54.

Modeling 3-d compliant blood flow with FOSLS, J. J. Heys, C. G. DeGroff, T. Manteuffel, S. McCormick, and H. Tufo, Biomed. Sci. Instr. 40 (2004), pp. 193-199.

2005

Analysis of first-order system least squares (FOSLS) for elliptic problems with discontinuous coefficients: Part I, M. Berndt, T. Manteuffel, S. McCormick, and G. Starke, SIAM J. Numer. Anal. 43 (2005), pp. 386-408.

Analysis of first-order system least squares (FOSLS) for elliptic problems with discontinuous coefficients: Part II, M. Berndt, T. Manteuffel, and S. McCormick, SIAM J. Numer. Anal. 43 (2005), pp. 409-436.

Numerical conservation properties of H(div)-conforming least-squares finite element methods for the Burgers equation, H. de Sterck, T. Manteuffel, S. McCormick, and L. Olson, SIAM J. Sci Comp. 26 (2005), pp. 1573-1597.

2006

A least-squares finite element method for the linear Boltzmann equation with anisotropic scattering, T. Austin and T. Manteuffel, SIAM J. Num. Anal. 44 (2006), pp. 540-560.

First-order system least squares (FOSLS) for geometrically nonlinear elasticity, T. Manteuffel, S. McCormick, J. Schmidt, and C. Westphal SIAM J. Numer. Anal. 44 (2006), pp. 2057-2081.

First-order system least squares (FOSLS) for modeling blood flow, J. J. Heys, C. G. DeGroff, T. Manteuffel, and S. McCormick, Med. Eng. Phys. 28 (2006), pp. 495-503.

First-order system least-squares for the Oseen equations, S.-D. Kim, C.-O. Lee, T. Manteuffel, S. McCormick, and O. Roehrle, J. Numer. Lin. Alg. Appl. 13 (2006), pp. 461-486.

First-order system LL* (FOSLL*) for general scalar elliptic problems in the plane, T. Manteuffel, S. McCormick, J. Ruge, and J. G. Schmidt, SIAM J. Num. Anal. 43 (2006), pp. 2098-2120.

On mass-conserving least-squares methods, J. Heys, E. Lee, T. Manteuffel, and S. McCormick, SIAM J. Sci. Comp. 28 (2006), pp. 1675-1693.

2007

FOSLL* method for the eddy current problem with three dimensional edge singularities, E. Lee and T. Manteuffel, SIAM J. Numer. Anal. 45 (2007), pp. 787-809.

Spatial multigrid for isotropic neutron transport, B. Chang, T. Manteuffel, S. McCormick, J. Ruge, and B. Sheehan, SIAM J. Sci. Comp. 29 (2007), pp. 1900-1917.

2008

An alternative least-squares formulation of the Navier-Stokes equations with improved mass conservation, J. Heys, E. Lee, T. Manteuffel, and S. McCormick, J. Comp. Phys. 226 (2008), pp. 994-1006.

Efficiency-based h- and hp-refinement strategies for finite element methods, H. De Sterck, T. Manteuffel, S. McCormick, J. Nolting, J. Ruge, and L. Tang, J. Num. Lin. Alg. Appl. 15 (2008), pp. 249-270.

2009

Enhanced mass conservation in least-squares methods for Navier-Stokes equations, J. Heys, E. Lee, T. Manteuffel, S. McCormick, and J. Ruge, SIAM J. Sci. Comp. 31 (2009), pp. 2303-2321.

2010

An efficiency-based adaptive refinement scheme applied to incompressible, resistive magnetohydrodynamics, J. Adler, T. Manteuffel, S. McCormick, J. Nolting, J. Ruge, and L. Tang, Lecture Notes in Computer Science 5910 (2010), pp. 1-13.

First-order system least squares for resistive magnetohydrodynamics, J. Adler, T. Manteuffel, S. McCormick, and J. Ruge, SIAM J. Sci. Comp. 32 (2010), pp. 229-248.

Further results on error estimators for local refinement with first-order system least squares (FOSLS), T. Manteuffel, S. McCormick, J. Nolting, J. Ruge, and G. Sanders, J. Num. Lin. Alg. Appl. 17 (2010), pp. 387-413.

Nested iteration and first-order system least squares for incompressible, resistive magnetohydrodynamics, J. Adler, T. Manteuffel, S. McCormick, J. Ruge, and G. Sanders, SIAM J. Sci. Comp. 32 (2010), pp. 1506-1526.

Weighted least-squares finite elements for particle imaging velocimetry analysis, M. Belohlavek, J. Heys, T. Mantueffel,S. McCormick, M. Milano, and E. McMahon, JCP 229 (2010), pp. 107-118.

Weighted-norm first-order system least squares for problems with corner singularities, E. Lee, T. Manteuffel, and C. Westphal, manuscript (2010).

2011

Efficiency-based adaptive local refinement for first-order system least-squares formulations, J. Adler, T. Manteuffel, S. McCormick, J. Nolting, J. Ruge, and L. Tang, SIAM J. Sci. Comp. 33 (2011), pp. 1-24 .

Parallel adaptive mesh refinement for first-order system least squares, M. Brezina, J. Garcia, T. Manteuffel, S. McCormick, J. Ruge, and L. Tang, J. Num. Lin. Alg. Appl., submitted (2011).