FOSLS manuscripts

FOSLoSophy.ps
First-order system least squares philosophy, manuascript by the FOSLS gang. [Written to provide basic understanding and encourage discussion.]
adapt.ps
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.
adapt2.pdf
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 .
bloodflo2d.pdf
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.
bloodflo3d.pdf
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.
bloodflow.pdf
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.
coupled1.pdf
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.
cd.ps
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.
disc-coef1.pdf
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.
disc-coef2.pdf
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.
divfree.pdf
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.
egg.ps or egg.pdf
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.
eit1.ps
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
eit2.ps
First-order system least squares and electrical impedance tomography: part II, H. MacMillan, S. McCormick, and T. Manteuffel, manuscript.
elas1.ps
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.
elas2.ps
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.
elas3.ps
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.
elas4.ps
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.
elliptic1.ps
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.
elliptic2.ps
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.
fosllt.ps
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.
fosllt2.pdf
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.
fosllt3.pdf
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.
helmholtz1.ps
Multilevel first-order system least squares (FOSLS) for Helmholtz equations, S. McCormick, Procs. Conf. Maxwell Equations, D.C., John Wiley and Sons, 1993.
helmholtz2.ps
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.
hpefficiency.pdf
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.
hyp1.pdf
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.
hyp2.pdf
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.
mass.pdf
On mass-conserving least-squares methods, J. Heys, E. Lee, T. Manteuffel, and S. McCormick, SIAM J. Sci. Comp. 28 (2006), pp. 1675-1693.
mass2.pdf
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. 9941006.
mhd1.pdf
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.
mhd2.pdf
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.
mhd3.pdf
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.
nitsche.ps
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.
nonlinear.ps or nonlinear.pdf
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.
nonlinelas.pdf
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.
nsfosll.pdf
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.
nstokes1.ps
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.
nstokes2.ps
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.
oseen.pdf
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.
piv.pdf
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.
refine.pdf
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.
stokes1.ps
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.
stokes2.ps
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.
trans1.ps
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.
trans4.pdf
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.
trans5.pdf
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.
weighted.pdf
Weighted-norm first-order system least squares for problems with corner singularities, E. Lee, T. Manteuffel, and C. Westphal.