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.

Finite element methods based on least squares and modified variational principles. COM²MAC 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.

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.

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 C⁰ 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.

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

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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