HR job title
- Professor
- Contact Info
- 1 979 595 5395
Popov, Bojan Professor
Positions
- Professor, Mathematics, College of Arts and Sciences
My research focuses on Conservation Laws, Linear Transport Equations, Approximation Theory, and Numerical Analysis of PDEs.
- Overview
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- Research
- Teaching
- Works By Students
- Background
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Overview
Publications
selected publications
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academic article
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Guermond, J., Nazarov, M., & Popov, B.
(2024).
Finite element-based invariant-domain preserving approximation of hyperbolic systems: Beyond second-order accuracy in space. Computer Methods in Applied Mechanics and Engineering.
418, 116470-116470.
-
Clayton, B., Guermond, J., Maier, M., Popov, B., & Tovar, E. J.
(2023).
Robust second-order approximation of the compressible Euler equations with an arbitrary equation of state. Journal of Computational Physics.
478, 111926-111926.
-
Guermond, J., Kees, C., Popov, B., & Tovar, E.
(2022).
Hyperbolic relaxation technique for solving the dispersive Serre-Green-Naghdi equations with topography. Journal of Computational Physics.
450, 110809-110809.
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Clayton, B., Guermond, J., & Popov, B.
(2022).
INVARIANT DOMAIN-PRESERVING APPROXIMATIONS FOR THE EULER EQUATIONS WITH TABULATED EQUATION OF STATE. SIAM Journal on Scientific Computing.
44(1), A444-A470.
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Guermond, J., Kronbichler, M., Maier, M., Popov, B., & Tomas, I.
(2022).
On the implementation of a robust and efficient finite element-based parallel solver for the compressible Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering.
389, 114250-114250.
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Guermond, J., Popov, B., & Saavedra, L.
(2021).
Second-Order Invariant Domain Preserving ALE Approximation of Euler Equations. 5(2), 923-945.
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Guermond, J., Maier, M., Popav, B., & Tomas, I.
(2021).
Second-order invariant domain preserving approximation of the compressible Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering.
375, 113608-113608.
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Popov, B., & Hua, Y.
(2021).
INVARIANT DOMAIN PRESERVING CENTRAL SCHEMES FOR NONLINEAR HYPERBOLIC SYSTEMS. COMMUNICATIONS IN MATHEMATICAL SCIENCES.
19(2), 529-556.
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Guermond, J., Popov, B., & Ragusa, J.
(2020).
POSITIVE AND ASYMPTOTIC PRESERVING APPROXIMATION OF THE RADIATION TRANSPORT EQUATION. SIAM Journal on Numerical Analysis.
58(1), 519-540.
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Guermond, J., Popov, B., & Saavedra, L.
(2020).
Second-order invariant domain preserving ALE approximation of hyperbolic systems. Journal of Computational Physics.
401, 108927-108927.
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Guermond, J., Popov, B., Tovar, E., & Kees, C.
(2019).
Robust explicit relaxation technique for solving the Green-Naghdi equations. Journal of Computational Physics.
399, 108917-108917.
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Guermond, J., Popov, B., & Tomas, I.
(2019).
Invariant domain preserving discretization-independent schemes and convex limiting for hyperbolic systems. 347, 143-175.
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Guermond, J., Klingenberg, C., Popov, B., & Tomas, I.
(2019).
The Suliciu approximate Riemann solver is not invariant domain preserving. Journal of Hyperbolic Differential Equations.
16(1), 59-72.
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Guermond, J., Nazarov, M., Popov, B., & Tomas, I.
(2018).
SECOND-ORDER INVARIANT DOMAIN PRESERVING APPROXIMATION OF THE EULER EQUATIONS USING CONVEX LIMITING. SIAM Journal on Scientific Computing.
40(5), A3211-A3239.
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Guermond, J., de Luna, M. Q., Popov, B., Kees, C. E., & Farthing, M. W.
(2018).
WELL-BALANCED SECOND-ORDER FINITE ELEMENT APPROXIMATION OF THE SHALLOW WATER EQUATIONS WITH FRICTION. SIAM Journal on Scientific Computing.
40(6), A3873-A3901.
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Guermond, J., Popov, B., & Yang, Y.
(2017).
The Effect of the Consistent Mass Matrix on the Maximum-Principle for Scalar Conservation Equations. Journal of Scientific Computing.
70(3), 1358-1366.
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Guermond, J., & Popov, B.
(2017).
INVARIANT DOMAINS AND SECOND-ORDER CONTINUOUS FINITE ELEMENT APPROXIMATION FOR SCALAR CONSERVATION EQUATIONS. SIAM Journal on Numerical Analysis.
55(6), 3120-3146.
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Guermond, J., Popov, B., Saavedra, L., & Yang, Y.
(2017).
INVARIANT DOMAINS PRESERVING ARBITRARY LAGRANGIAN EULERIAN APPROXIMATION OF HYPERBOLIC SYSTEMS WITH CONTINUOUS FINITE ELEMENTS. SIAM Journal on Scientific Computing.
39(2), A385-A414.
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Azerad, P., Guermond, J., & Popov, B.
(2017).
WELL-BALANCED SECOND-ORDER APPROXIMATION OF THE SHALLOW WATER EQUATION WITH CONTINUOUS FINITE ELEMENTS. SIAM Journal on Numerical Analysis.
55(6), 3203-3224.
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Guermond, J., & Popov, B.
(2016).
Fast estimation from above of the maximum wave speed in the Riemann problem for the Euler equations. 321, 908-926.
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Guermond, J., Popov, B., & Tomov, V.
(2016).
Entropy-viscosity method for the single material Euler equations in Lagrangian frame. Computer Methods in Applied Mechanics and Engineering.
300, 402-426.
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Guermond, J., & Popov, B.
(2016).
ERROR ESTIMATES OF A FIRST-ORDER LAGRANGE FINITE ELEMENT TECHNIQUE FOR NONLINEAR SCALAR CONSERVATION EQUATIONS. SIAM Journal on Numerical Analysis.
54(1), 57-85.
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Guermond, J., & Popov, B.
(2016).
INVARIANT DOMAINS AND FIRST-ORDER CONTINUOUS FINITE ELEMENT APPROXIMATION FOR HYPERBOLIC SYSTEMS. SIAM Journal on Numerical Analysis.
54(4), 2466-2489.
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Guermond, J., & Popov, B.
(2015).
Entropy Viscosity and L1-based Approximations of PDEs: Exploiting Sparsity
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Popov, B., & Tomov, V.
(2015).
CENTRAL SCHEMES FOR MEAN FIELD GAMES. COMMUNICATIONS IN MATHEMATICAL SCIENCES.
13(8), 2177-2194.
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Bonito, A., Guermond, J., & Popov, B.
(2014).
STABILITY ANALYSIS OF EXPLICIT ENTROPY VISCOSITY METHODS FOR NON-LINEAR SCALAR CONSERVATION EQUATIONS. Mathematics of Computation.
83(287), 1039-1062.
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Guermond, J., Nazarov, M., Popov, B., & Yang, Y.
(2014).
A SECOND-ORDER MAXIMUM PRINCIPLE PRESERVING LAGRANGE FINITE ELEMENT TECHNIQUE FOR NONLINEAR SCALAR CONSERVATION EQUATIONS. SIAM Journal on Numerical Analysis.
52(4), 2163-2182.
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Guermond, J., & Popov, B.
(2014).
VISCOUS REGULARIZATION OF THE EULER EQUATIONS AND ENTROPY PRINCIPLES. SIAM Journal on Applied Mathematics.
74(2), 284-305.
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Zingan, V., Guermond, J., Morel, J., & Popov, B.
(2013).
Implementation of the entropy viscosity method with the discontinuous Galerkin method. Computer Methods in Applied Mechanics and Engineering.
253, 479-490.
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Mehmetoglu, O., & Popov, B.
(2012).
MAXIMUM PRINCIPLE AND CONVERGENCE OF CENTRAL SCHEMES BASED ON SLOPE LIMITERS. Mathematics of Computation.
81(277), 219-231.
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Guermond, J., Pasquetti, R., & Popov, B.
(2011).
From Suitable Weak Solutions to Entropy Viscosity. Journal of Scientific Computing.
49(1), 35-50.
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Guermond, J., Pasquetti, R., & Popov, B.
(2011).
Entropy viscosity method for nonlinear conservation laws. Journal of Computational Physics.
230(11), 4248-4267.
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Kopotun, K. A., & Popov, B.
(2010).
Moduli of smoothness of splines and applications in constrained approximation. Jaen Journal on Approximation.
2(1), 79-91.
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Dobrev, V., Guermond, J., & Popov, B.
(2010).
SURFACE RECONSTRUCTION AND IMAGE ENHANCEMENT VIA L-1-MINIMIZATION. SIAM Journal on Scientific Computing.
32(3), 1591-1616.
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Guermond, J., & Popov, B.
(2009).
AN OPTIMAL L(1)-MINIMIZATION ALGORITHM FOR STATIONARY HAMILTON-JACOBI EQUATIONS. COMMUNICATIONS IN MATHEMATICAL SCIENCES.
7(1), 211-238.
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Christov, I., & Popov, B.
(2008).
New non-oscillatory central schemes on unstructured triangulations for hyperbolic systems of conservation laws. 227(11), 5736-5757.
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Guermond, J., & Popov, B.
(2008).
L-1-minimization methods for Hamilton-Jacobi equations: the one-dimensional case. Numerische Mathematik.
109(2), 269-284.
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Guermond, J., Marpeau, F., & Popov, B.
(2008).
Fast algorithm for solving first-order PDES by L-1-minimization. COMMUNICATIONS IN MATHEMATICAL SCIENCES.
6(1), 199-216.
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Guermond, J., & Popov, B.
(2008).
L-1-APPROXIMATION OF STATIONARY HAMILTON-JACOBI EQUATIONS. SIAM Journal on Numerical Analysis.
47(1), 339-362.
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Guermond, J., & Popov, B.
(2007).
Linear advection with ill-posed boundary conditions via L-1-minimization. INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING.
4(1), 39-47.
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Kurganov, A., Petrova, G., & Popov, B.
(2007).
Adaptive semidiscrete central-upwind schemes for nonconvex hyperbolic conservation laws. SIAM Journal on Scientific Computing.
29(6), 2381-2401.
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Popov, B., & Trifonov, O.
(2006).
One-sided stability and convergence of the Nessyahu-Tadmor scheme. Numerische Mathematik.
104(4), 539-559.
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Popov, B., & Trifonov, O.
(2006).
Order of convergence of second order schemes based on the minmod limiter. Mathematics of Computation.
75(256), 1735-1753.
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Efendiev, Y., & Popov, B.
(2005).
On homogenization of nonlinear hyperbolic equations. Communications on Pure and Applied Analysis.
4(2), 295-309.
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Konyagin, S., Popov, B., & Trifonov, O.
(2005).
On convergence of minmod-type schemes. SIAM Journal on Numerical Analysis.
42(5), 1978-1997.
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Liu, J. G., Popov, B., Hong, H., & Ewing, R. E.
(2005).
Convergence analysis of wavelet schemes for convection-reaction equations under minimal regularity assumptions. SIAM Journal on Numerical Analysis.
43(2), 521-539.
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Kopotun, K., Neamtu, M., & Popov, B.
(2003).
Weakly nonoscillatory schemes for scalar conservation laws. Mathematics of Computation.
72(244), 1747-1767.
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Petrova, G., & Popov, B.
(2001).
Linear Transport Equations with -Monotone Coefficients. Journal of Mathematical Analysis and Applications.
260(2), 307-324.
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Petrova, G., & Popov, B.
(1999).
Linear transport equations with discontinuous coefficients. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS.
24(9-10), 1849-1873.
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Kostenko, S. B., & Popov, B. A.
(1993).
Uniform approximation of modified Bessel function. Fiziko-Khimicheskaya Mekhanika Materialov.
29(6), 125-127.
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Popov, B. A.
(1993).
Methods for determining node location in asymptotically uniform spline approximation. Journal of Mathematical Sciences: a translation of selected Russian-language serial publications in mathematics.
66(5), 2451-2458.
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Sokolov, V. M., Koval'chuk, L. A., Popov, B. A., & Balkovoi, Y. V.
(1989).
Activity of nitrogen and sulfur in metallic melts. Russian Metallurgy.
27-32.
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Sokolov, V. M., Tesler, G. S., Popov, B. A., & Koval'chuk, L. A.
(1988).
Temperature dependence of the activity coefficient of carbon in multicomponent iron-based melts. 1(1), 43-46.
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Sokolov, V. M., Tesler, G. S., Popov, B. A., & Koval'chuk, L. A.
(1987).
CALCULATION OF THE SOLUBILITY-TEMPERATURE RELATIONSHIP FOR NITROGEN IN NICKEL MELTS. Russian Metallurgy.
36-41.
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Yarema, S. Y., Mel'nichok, L. S., & Popov, B. A.
(1984).
Dispersion in fatigue crack growth rate and processing of experimental data. Materials Science.
20(3), 259-265.
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Guermond, J., Nazarov, M., & Popov, B.
(2024).
Finite element-based invariant-domain preserving approximation of hyperbolic systems: Beyond second-order accuracy in space. Computer Methods in Applied Mechanics and Engineering.
418, 116470-116470.
-
chapter
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Popov, P., & Popov, B.
(2009).
A Second Order Central Scheme for Hamilton-Jacobi Equations on Triangular Grids. Lecture Notes in Artificial Intelligence.
Numerical Analysis and Its Applications.
(pp. 476-485).
Springer Nature.
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Christov, I., Mishev, I. D., & Popov, B.
(2009).
Finite volume methods on unstructured Voronoi meshes for hyperbolic conservation laws. Hyperbolic Problems: Theory, Numerics and Applications.
(pp. 507-+).
American Mathematical Society (AMS).
-
Popov, P., & Popov, B.
(2009).
A Second Order Central Scheme for Hamilton-Jacobi Equations on Triangular Grids. Lecture Notes in Artificial Intelligence.
Numerical Analysis and Its Applications.
(pp. 476-485).
Springer Nature.
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conference paper
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Pasquetti, R., Guermond, J. L., & Popov, B.
(2015).
Stabilized Spectral Element Approximation of the Saint Venant System Using the Entropy Viscosity Technique. Lecture Notes in Computational Science and Engineering.
397-404.
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Guermond, J., & Popov, B.
(2014).
ENTROPY VISCOSITY FOR THE EULER EQUATIONS AND QUESTIONS REGARDING PARABOLIC REGULARIZATION. 119-124.
-
Guermond, J., Pasquetti, R., & Popov, B.
(2011).
From suitable weak solutions to entropy viscosity. Ercoftac Series.
373-+.
-
Popov, P., & Popov, B.
(2009).
A Second Order Central Scheme for Hamilton-Jacobi Equations on Triangular Grids. Lecture Notes in Artificial Intelligence.
476-+.
-
Dobrev, V., Guermond, J., & Popov, B.
(2009).
Surface Reconstruction via L(1)-Minimization. Lecture Notes in Artificial Intelligence.
32-43.
-
Popov, B.
(1996).
Nonlinear best Chebyshev approximations and splines. 128-131.
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Pasquetti, R., Guermond, J. L., & Popov, B.
(2015).
Stabilized Spectral Element Approximation of the Saint Venant System Using the Entropy Viscosity Technique. Lecture Notes in Computational Science and Engineering.
397-404.
-
institutional repository document
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Clayton, B., Guermond, J., Maier, M., Popov, B., & Tovar, E. J.
(2022).
Robust second-order approximation of the compressible Euler equations with an arbitrary equation of state
-
Guermond, J., Kronbichler, M., Maier, M., Popov, B., & Tomas, I.
(2021).
On the implementation of a robust and efficient finite element-based parallel solver for the compressible Navier-Stokes equations
-
Guermond, J., Kees, C., Popov, B., & Tovar, E.
(2021).
Hyperbolic relaxation technique for solving the dispersive Serre-Green-Naghdi Equations with topography
-
Guermond, J., Popov, B., & Ragusa, J.
(2019).
Positive asymptotic preserving approximation of the radiation transport equation
-
Guermond, J., Popov, B., & Tomas, I.
(2018).
Invariant domain preserving discretization-independent schemes and convex limiting for hyperbolic systems
-
Guermond, J., Nazarov, M., Popov, B., & Tomas, I.
(2017).
Second-order invariant domain preserving approximation of the Euler equations using convex limiting
-
Guermond, J., & Popov, B.
(2015).
Fast estimation from above of the maximum wave speed in the Riemann problem for the Euler equations
-
Guermond, J., & Popov, B.
(2015).
Invariant domains and first-order continuous finite element approximation for hyperbolic systems
-
Clayton, B., Guermond, J., Maier, M., Popov, B., & Tovar, E. J.
(2022).
Robust second-order approximation of the compressible Euler equations with an arbitrary equation of state
Research
principal investigator on
- High-Order Invariant Domain Preserving-Numerical Methods for Nonlinear Hyperbolic Systems- awarded by National Science Foundation - (Arlington, Virginia, United States) 2016 - 2020
- High-Order Approximation Techniques for Nonlinear Hyperbolic Pdes awarded by National Science Foundation - (Arlington, Virginia, United States) 2012 - 2016
co-principal investigator on
- Robust approximation of nonlinear conservation equations awarded by United States Army - (Washington D.C., District of Columbia, United States) 2019 - 2023
- Robust and Accurate Approximation of Hyperbolic Systems awarded by United States Air Force - (Arlington, Virginia, United States) 2018 - 2021
- Finite Element Approximation of Nonlinear Systems Developing Shocks, Fronts and Interfaces awarded by United States Army - (Washington D.C., District of Columbia, United States) 2015 - 2019
- Robust Approximation of Nonlinear Hyperbolic Systems awarded by United States Air Force - (Arlington, Virginia, United States) 2015 - 2017
- Entropy Viscosity and L-1 Based Approximations of Pdes: Exploiting Sparsity awarded by United States Air Force - (Arlington, Virginia, United States) 2012 - 2015
Teaching
teaching activities
- MATH304 Linear Algebra Instructor
- MATH308 Differential Equations Instructor
- MATH309 Linear Alg For Diff Eq Instructor
- MATH412 Theory Of Pdes Instructor
- MATH417 Numerical Methods Instructor
- MATH437 Princ Of Numerical Analy Instructor
- MATH485 Directed Studies Instructor
- MATH491 Hnr-research Instructor
- MATH602 Meth Appl Part Diff Eq Instructor
- MATH609 Numerical Analysis Instructor
- MATH638 Conservation Laws Instructor
- MATH685 Directed Studies Instructor
- MATH691 Research Instructor
Works By Students
chaired theses and dissertations
-
Mehmetoglu, Orhan (2012-10). Stability and Convergence of High Order Numerical Methods for Nonlinear Hyperbolic Conservation Laws.
-
Tomov, Vladimir (2014-04). Entropy Viscosity Method for Lagrangian Hydrodynamics and Central Schemes for Mean Field Games.
Background
education and training
Contact
first name
- Bojan
has last name
- Popov
mailing address
-
Texas A&M University
Mathematics
3368 TAMU
College Station, TX 77843-3368
USA
Other
- popov@tamu.edu