Please note that some earlier papers are not available in electronic format.
E-mail me if you would like a copy. You can download bibtex bibiography file for all these papers.
### Books
**Finite element methods based on
least squares and modified variational
principles**.
COM^{2}MAC Lecture Notes, Postech, Pohang, South
Korea, 2001.
Download
PDF.
**
****Compatible spatial discretizations**,
Proceedings of IMA Hot
Topics workshop on Compatible discretizations, IMA Volume 142,
Springer Verlag, eds. D. Arnold, P. Bochev, R. Lehoucq, R. Nicolaides
and M. Shashkov, 2006.
**Least-Squares Finite Element Methods**. Series: Applied Mathematical Sciences , Vol. 166. Bochev, Pavel B., Gunzburger, Max D. 2009, X, 670 p., Hardcover ISBN: 978-0-387-30888-3.
### Book chapters
**A discourse on variational and geometric aspects of
stability of discretizations.** In: *33rd
Computational Fluid Dynamics Lecture Series*, VKI LS 2003-05, edited
by H. Deconinck, ISSN0377-8312. Von Karman
Institute for Fluid Dynamics, Chaussee de Waterloo, 72, B-1640 Rhode Saint
Genese, Belgium. 90 pages. Download PDF.
**Matching algorithms with physics: exact sequences of
finite element spaces** (with A. Robinson).
In: *Collected lectures on preservation of stability under discretization*,
edited by D. Estep and S. Tavener, SIAM, Philadelphia, 2001.
Download PDF.
**Least-squares/penalty finite element methods for
optimization and control problems** (with M.
Gunzburger), To appear in: *Proceedings of the workshop "Towards real time
and online PDE constrained optimization"* Santa Fe, 2005, SIAM,
Philadelphia. Download PDF.
**Principles of mimetic discretizations,** (with M. Hyman), SAND 2005-3340P,
2005, in IMA Volume 142, Springer Verlag, eds. D. Arnold, P. Bochev, R.
Lehoucq, R. Nicolaides and M. Shashkov, 2006. Download
PDF.**
**
, **Blending methods for coupling atomistic and continuum models**. S. Badia, P.Bochev, M. Gunzburger, R. Lehoucq and M. Parks. In: *Bridging the scales in science and engineering, *edited by J. Fish, Oxford University Press, 2008.
### Refereed papers
**Application of the extended interval arithmetic to a real initial value
problem**, Annuaire Univ. Sofia Fac. Math.
Inform. 81 (1987), no. 1, 167--180 (1994); MR 95f:65096
**Safe and accurate computation of the matrix
exponential, ***Numerical Methods and
Applications,* Sofia, 1988, Publishing House of the Bulgarian Academy
of Sciences, (Sofia, 1989), pp.65-69.
**Highly accurate and safe numerical computations via
interval analysis and advanced computer arithmetic** (with** **R. Angelov,
G. Grozev, and S. Markov). In *Numerical
methods and applications* (Sofia, 1989), 23-27, Publ. House Bulgar.
Acad. Sci., (Sofia, 1989); CNO 1027605
**A self-validating numerical method for the matrix
exponential **(with S. Markov), *Computing*
43 (1989), no. 1, 59--72; MR 90i:65072
**Enclosure methods for set valued phase flow**, in *Contributions to computer arithmetic and
self-validating numerical methods* (Basel, 1989), 173--181, Baltzer, Basel, 1990; MR 92h:65070
**Simultaneous self-verified computation of**
**and**
,
*Computing* 45 (1990), no. 2, 183--191; MR 91i:65058
**Accuracy of least-squares methods for the
Navier-Stokes equations** (with** **M. Gunzburger), *Comput. Fluids* 22
(1993), no. 4-5, 549--563; MR 94e:76053
**Analysis of least squares finite element methods for
the Stokes equations **(with M. Gunzburger),
*Math. Comp.* 63 (1994), no. 208, 479--506; MR 95c:76060. Download
PDF.
**A least squares finite element method for the Navier-Stokes equations** (with M. Gunzburger) *Appl. Math. Lett.*
6
(1993), no. 2, 27--30; MR 96e:76077
**Least-squares methods for the
velocity-pressure-stress formulation of the Stokes equations** (with M. Gunzburger), *Comput. Methods Appl. Mech.
Engrg.* 126 (1995), no. 3-4, 267--287; MR
96g:76034. Download PDF.
**Analysis and computation of adaptive moving grids by
deformation** (G. Liao, and G. dela Pena), *Numer.
Methods Partial Differential Equations* 12 (1996), no. 4, 489--506; MR 97c:65161. Download PDF.
**On quadratic invariants and symplectic structure** (with C. Scovel) *BIT* 34 (1994), no.
3, 337--345; MR 97k:65164. Download PDF.
**Analysis of least-squares finite element methods for
the Navier-Stokes equations**, *SIAM J.
Numer. Anal.* 34 (1997),
no. 5, 1817--1844; MR 98g:76053. Download PDF.
**Least-squares methods for optimal control**, *Nonlinear Anal.* 30 (1997), no. 3,
1875--1885; CNO 1490097. Download PDF.
**Least-squares methods for Navier-Stokes boundary
control problems** (with D. Bedivan) *Int.
J. Comput. Fluid Dyn*. 9
(1997), no. 1, 43--58; MR 98k:76084
**Experiences with negative norm least-square methods for the Navier-Stokes equations**, *Electron. Trans. Numer. Anal.* 6 (1997), Dec., 44--62 (electronic);
MR 99a:76081. Download PDF.
**Least-squares finite element methods for viscous,
incompressible flows** (with M. Gunzburger)
ASME Paper FEDSM97-3487, *1997 ASME Fluids Engineering Division Summer
Meeting, *(Vancouver, 1997), Vancouver, British Columbia, June 22-26,
1997.
Download PDF.
**Analysis of velocity-flux first-order system
least-squares principles for the Navier-Stokes equations. I** (with Z. Cai, T. Manteuffel, and S. McCormick) *SIAM
J. Numer. Anal.* 35
(1998), no. 3, 990--1009 (electronic); MR
99a:76106. Download PDF.
**Finite element methods of least-squares type** (with M. Gunzburger) *SIAM Review* 40
(1998), no. 4, 789--837
(electronic); MR 99k:65104. Download PDF.
**Least-squares methods for the Navier-Stokes
equations: trends and developments**, in *Proceedings
of the 2*^{nd} European Conference on Numerical Methods and Applications
*ENUMATH 97*, Heidelberg, September 29-
October 3, 1997, Edited by H. Bock, G. Kansacht, R. Rannacher, F. Brezzi, R.
Glowinski, Y. Kuznetsov and J. Periaux, pp.172--179, World Sci. Publishing,
River Edge, NJ, 1998; CNO 1705030, ISBN:981-02-3546-1. Download
PDF.
**Negative norm least-squares methods for the
velocity-vorticity-pressure Navier-Stokes equations**, *Numer. Methods Partial Differential Equations* 15
(1999), no. 2, 237--256; MR
2000a:65106. Download PDF.
**Analysis of velocity-flux least-squares principles
for the Navier-Stokes equations. II** (with
T. Manteuffel, and S. McCormick) *SIAM J. Numer. Anal.* 36 (1999), no. 4, 1125--1144 (electronic);
MR 2000b:76064. Download PDF.
**Improved least-squares error estimates for scalar
hyperbolic problems** (with J. Choi), *Comput.
Methods Appl. Math.* 1 (2001), no. 2, 115--124; MR 2002g:65139. Download PDF.
**A comparative study of least squares, SUPG and
Galerkin methods for convection problems**
(with J. Choi), *Int. J. Comput. Fluid Dyn.* 15 (2001), no. 2,
127--146; MR 2002m:76066
**On stabilized finite element methods for transient
problems with varying time scales. **(with**
**J. Shadid and M. D. Gunzburger), *Proceedings of the Fifth World
Congress on Computational Mechanics* (WCCM V), July 7-12, 2002,
Vienna, Austria, Editors: Mang, H.A.; Rammerstorfer, F.G.;
Eberhardsteiner, J., Publisher: Vienna University of Technology, Austria,
ISBN 3-9501554-0-6, http://wccm.tuwien.ac.at
**Regularized formulations of FETI** (with R. Lehoucq) in *Domain Decomposition
methods in Science and Engineering,* I. Herera, D. Kayes, O. Widlund
and R. Yates (Eds.), National Autonomous University of Mexico (UNAM), 2003,
ISBN970-32-0859-2, pp.203-209. Download PDF.
**Towards robust 3D Z-pinch simulations: discretizations
and fast solvers for magnetic diffusion in heterogeneous conductors** (with J. Hu, A. Robinson and R. Tuminaro) *ETNA*,
Vol. 15, pp.186-210, 2003. Download
PDF
**An improved algebraic multigrid method for solving
Maxwell's equations** (with C. Garasi, J.
Hu, A. Robinson and R. Tuminaro) *SIAM J. Sci. Comp.* 25/2, pp.
623-642, 2004. Download PDF.
**A taxonomy of stabilized FEM for the Stokes problem** (with T. Barth, M. Gunzburger and J. Shadid) *SIAM
J. Sci. Comp*., 25/5, pp.1585-1607, 2004. Download
PDF.
**An absolutely stable pressure-Poisson stabilized
finite element method for the Stokes equations** (with M. Gunzburger) *SIAM J. Num. Anal.* 42/3, pp.
1189-1207 (2005). Download
PDF.
**On inf-sup stabilized finite element methods for
transient problems** (with M. Gunzburger and
J. Shadid) *Comp. Meth. Appl. Mech. Engrg.* Volume: 193, Issue:
15-16, pp. 1471-1489, 2004. Download
PDF.
**Stability of the SUPG finite element method for
transient ****advection****-diffusion
problems** (with M. Gunzburger and J.
Shadid) *Comp. Meth. Appl. Mech. Engrg*. 193, Issues 23-26,
pp.2301-2323, 2004. Download PDF.
**Least-squares finite element methods for
optimization and control problems for the Stokes equations **(with M. Gunzburger) *Comp. Math. Appl.,*
Vol. 48, No.7, 2004, pp. 1035-1057. Download PDF.
**On the finite element solution of the pure Neumann
problem** (with R. Lehoucq) *SIAM Review*, 47/1, pp. 50-66, 2005. Download PDF.
**Constrained interpolation (remap) of divergence-free
fields** (with M. Shashkov) *Computer
Methods in Applied Mechanics and Engineering*, 194 (2005), pp.
511—530. Download
PDF.
**Least-squares finite element methods for first-order
elliptic systems**, *Int. J. Num. Anal.
Modeling*, Vol. 1, No. 1, pp. 49—64, 2004. Download PDF.
**Least-squares finite element methods for optimality systems
arising in optimization and control problems**
(with M. Gunzburger). *SIAM J. Num. Anal. * Vol. 43, No. 6, (2006), pp. 2517-2543.
Download
PDF.
**A stabilized finite element method for the Stokes
problem based on polynomial pressure projections** (with C. Dohrmann) *Int. J. Num. Meth. Fluids.* 46, pp.183-201,
2004. Download PDF.
**On least-squares finite element methods for the
Poisson equation and their connection to the Dirichlet and Kelvin principles** (with M. Gunzburger) *SIAM J. Num. Anal.*,
Vol. 43/1, pp. 340-362, 2005. Download
PDF.
**Stabilization of low-order mixed finite elements for
the Stokes equations** (with C. Dohrmann and
M.D. Gunzburger). *SIAM J. Num. Anal.* Vol. 44/1, pp.82-101, 2006. SAND 2004-2391J. Download
PDF.
**Toward an h-independent algebraic multigrid method
for ****Maxwells****
equations** (with J. Hu, R. Tuminaro, C.
Garasi, A. Robinson). *SIAM J. Sci. Comp.*
Vol. 27, No. 5, pp.1669-1688, 2006. SAND 2004-2134J.
Download
PDF.
**A computational study of stabilized, low order C**^{0}
finite element approximations of Darcy equations (with C. Dohrmann). To appear in *Computational Mechanics*.
Download PDF.
**Compatible discretizations of second-order elliptic
equations** (with M. Gunzburger) *Zapiski
Nauchnyh Seminarov POMI,* Vol. 318, Part 35, Boundary-Value Problems
of Mathematical Physics and Related Problems of Function Theory, S. Repin and
G. A. Seregin, eds. pp. 75-99, 2005. Download PDF.
**Compatible least-squares methods **(with M. Gunzburger). Submitted to *SIAM J. Num. Anal*.
**Regularization and stabilization of discrete
saddle-point variational problems** (with R.
Lehoucq). *ETNA.*, Vol. 22, pp. 97-113, 2006. Download PDF.
**A multiscale Discontinuous Galerkin method with the
computational structure of a continuous Galerkin method** (with T. Hughes, G. Scovazzi, and A. Buffa).
*CMAME*, Vol. 195, pp.2761-2787, 2006. SAND 2005-2124J.
. Download PDF.
**A Multiscale Discontinuous Galerkin Method** (with T. Hughes, and G. Scovazzi). *Proceedings
of LSSC 2005*, I. Lirkov, S. Margenov and J. Wasniewski (Eds.),
Springer Lecture Notes in Computer Science 3743, pp. 84-93, 2006. Download
PDF.
**Analysis and computation of least-squares methods
for a compressible Stokes problem** (with S.
Kim and B. Shin). *Num. Meth PDEs*, Volume 22, Issue 4, pp.867-883 2006. Download PDF.
**On least-squares variational principles for the
discretization of optimization and control problems** (with M. Gunzburger). *Methods and Applications of
Analysis*, Vol.12, No.4, pp.395-426, December 2005. SAND 2005-4939J. Download
PDF.
**On stabilized finite element methods for the Stokes
problem in the small time step limit** (with
M. Gunzburger and R. Lehoucq). *Int. J. Num. Meth. Fluids.*,
Volume 53, Issue 4, pp. 573-597, 2007. SAND 2005-7817J. DOI: 10.1002/fld.1295 Download PDF.
**Least-squares finite element methods** (with M. Gunzburger), *Proceedings of the
International Congress of Mathematicians* (ICM), Madrid 2006. Invited
Lectures. Download PDF.
**A least-squares method for consistent mesh tying** (with D. Day). *Int. J. Num. Anal. Model.* Volume 4, Issue 3-2, pp. 342-352. 2007.SAND 2006-1412J. Download PDF.
**A locally conservative least-squares method for Darcy flows** (with M. Gunzburger). *Communications in Numerical Methods in Engineering. *
SAND 2006-2097J. Published online December 1st, 2006; DOI: 10.1002/cnm.957. Download PDF.
**A novel Lagrange-multiplier based method for consistent mesh tying** (with M. Parks and L. Romero). CMAME, Vol. 196, Issues 35-36, pp. 3335–3347. (2007) SAND 2006-6840J. Download PDF.
**Connecting Atomistic-to-Continuum Coupling and Domain Decomposition** (with M. Parks and R. Lehoucq). Submitted to *SISC. *SAND 2007-0704J*. *Download PDF.
**Analysis and computation of a least-squares method for consistent mesh tying **(with D. Day). Published online 07/10/2007. __http://dx.doi.org/10.1016/j.cam.2007.04.049__ SAND 2007-1510J. Download PDF
**An algebraic multigrid approach based on a compatible gauge reformulation of Maxwell’s equations.** (With J. Hu, C. Siefert, R. Tuminaro). Submitted to SISC. SAND 2007-1633J. Download PDF
**A Force-Based Blending Model for Atomistic-to-Continuum Coupling.** (With S. Badia, J. Fish, M. Gunzburger, R. Lehoucq, M. Nuggehally and M. Parks). Accepted in International Journal for Multiscale Computational Engineering. SAND2007-1776J. Download PDF
**Finite Element Solution of Optimal Control problems Arising in Semiconductor Modeling**, (With D. Ridzal), to appear in Proceedings of LSSC 2007, I. Lirkov, S. Margenov and J. Wasniewski (Eds.), Springer Lecture Notes in Computer Science, 2008. SAND-2007-2936C. Download PDF
**On atomistic-to-continuum coupling by blending.** (With S. Badia, M. Parks, M. Gunzburger, and R. Lehoucq). Submitted to SIAM J. Multiscale Modeling and Simulation. SAND 2007-5126J.
**Bridging methods for coupling atomistic and continuum models. **(With S. Badia, M. Gunzburger, R. Lehoucq , and M. Parks). To appear in Proceedings of LSSC 2007, I. Lirkov, S. Margenov and J. Wasniewski (Eds.), Springer Lecture Notes in Computer Science, vol. 4818, 2008. SAND 2007-5383C.
**Rehabilitation of the lowest-order Raviart-Thomas element on quadrilateral grids.** (With D. Ridzal), SAND 2007-6297J. Submitted to SIAM J. Num. Anal.
### Other papers
**Interval analytic methods for solving ODE's** (in Bulgarian) (with S. Markov), *Proceedings of
the XIII National Workshop "Applications of Mathematics", *Varna,
1987, pp.200-203.
**Numerical methods with Result verification and
software environment for their realization**,
(in Bulgarian), (with T. Velitchkov and S. Markov).* Proceedings 18*^{th}
Spring Conference of the Union of Mathematicians in Bulgaria, (Albena, April 6-10, 1989), pp.67-79.
**Analysis of weighted least-squares finite element
methods for the Navier-Stokes equations**,
(with M. Gunzburger). *Proceedings of the 14*^{th} IMACS World
Congress, *Volume 2, Edited by W.F. Ames, *Georgia Tech, Atlanta, pp.584-587, 1994.
**First-order system least-squares for the
Navier-Stokes equations**, (with Z. Cai, T.
Manteuffel and S. McCormick), in *Proceedings of the Seventh Copper Mountain
Conference on Multigrid methods, *NASA Conference Publication 3339,
Part 1, pp.41-55, 1996.
**Least-squares methods for elliptic problems**, in *Proceedings of Conference on Iterative
Solution Methods for the Elasticity Equations as Arising in Mechanics and Biomechanics,
IMMB'98*, University of Nijmegen, Netherlands, September 28-30, 1998.
**Least-squares finite element methods with
applications to the Stokes equations**, (with
J. Deang and M. Gunzburger ), *Proceedings of the KAIST Mathematics workshop
on Finite Element Methods*, Edited by Do Young Kwak, KAIST, Daejon,
South Korea, February 1999, pp. 21-39.
**On stabilized finite element methods for transient
problems with varying time scales**. (with M.
Gunzburger and R. Lehoucq). *Proceedings of ECOMASS* *2004*.
**Stabilized finite element methods for the Stokes
problem based on polynomial pressure projections**. (with C. Dohrmann). *Proceedings of ECOMASS 2004.*
**Variational multiscale framework for DG**, (with T. Hughes, and G. Scovazzi ),ASME paper
IMECE2005-80894, *Proceedings of 2005 ASME International Mechanical
Engineering Congress and Exposition***, **Orlando Florida, 2005.
**Constrained interpolation remap of discrete
divergence free fields**. (with M. Shashkov).
*Proceedings of the Five-Laboratory Conference on Computational Mathematics*,
Vienna, Austria, 19– 23 June 2005 (2005). SAND 2005-3330C. Accepted
06/01/2005
**Application of algebraic topology to mimetic
discretizations**. (with M. Hyman). *Proceedings
of the Five-Laboratory Conference on Computational Mathematics*,
Vienna, Austria, 19– 23 June 2005 (2005). SAND 2005-3331C, Accepted
06/01/2005
### Technical reports
**Accuracy of least-squares methods for the
Navier-Stokes equations**, (with M.
Gunzburger) NASA Technical Memorandum, 106209, ICOMP-93-19, June 1993.
**On quadratic invariants and simplectic structure**, (with C. Scovel) LA-UR-93-3198, Los Alamos
National Laboratory, 1993
**Finite Element Methods: a variational approach to
theory and practice**, Sandia National
Laboratories, Report SAND2000-0979, SCAN Issue 2, July 2000, 133 pages.
**A Mathematical Framework for Multiscale Science and
Engineering: The Variational Multiscale Method and Interscale Transfer
Operators**, (with M. Christon, S. Collis,
R. Lehoucq, A. Slepoy, and J. Shadid). Sandia National Laboratories, Report
SAND2004-2871. Download
PDF.
**Geophysical Subsurface Imaging and Interface
Identification**, (with D. Day, K. Pendley,
C. Weiss, and A. Robinson). Sandia National Laboratories, Report SAND2005-6272,
2005
**Blended Atomistic-to-Continuum coupling analyses and methods.** (with S. Badia, M. Gunzburger, R. Lehoucq and M. Parks). Sandia National Laboratories, Report SAND2007-0905, 2007. Download PDF
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