# overview
My research focuses on Conservation Laws, Linear Transport Equations, Approximation Theory, and Numerical Analysis of PDEs.

# keywords[]
4903 Numerical And Computational Mathematics

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4007 Control Engineering, Mechatronics And Robotics

# keywords[]
4903 Numerical And Computational Mathematics

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4903 Numerical And Computational Mathematics

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Strong Stability Preserving Time Stepping

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4903 Numerical And Computational Mathematics

# keywords[]
4903 Numerical And Computational Mathematics

# educationAndTraining[].organization.label
University of South Carolina - (Columbia, South Carolina, United States)

# educationAndTraining[].organization.label
Technical University of Sofia - (Sofia, Bulgaria)

# publications[].label
The Suliciu approximate Riemann solver is not invariant domain preserving

# publications[].label
From Suitable Weak Solutions to Entropy Viscosity

# publications[].label
On homogenization of nonlinear hyperbolic equations

# publications[].publisher
American Institute of Mathematical Sciences (AIMS)

# publications[].label
Robust explicit relaxation technique for solving the Green-Naghdi equations

# publications[].label
New non-oscillatory central schemes on unstructured triangulations for hyperbolic systems of conservation laws

# publications[].label
INVARIANT DOMAINS AND SECOND-ORDER CONTINUOUS FINITE ELEMENT APPROXIMATION FOR SCALAR CONSERVATION EQUATIONS

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
L-1-minimization methods for Hamilton-Jacobi equations: the one-dimensional case

# publications[].label
Well-Balanced Second-Order Convex Limiting Technique for Solving the SerreGreenNaghdi Equations

# publications[].label
On the implementation of a robust and efficient finite element-based  parallel solver for the compressible Navier-Stokes equations

# publications[].label
Uniform approximation of modified Bessel function

# publications[].label
Invariant domain preserving discretization-independent schemes and  convex limiting for hyperbolic systems

# publications[].label
Stabilized Spectral Element Approximation of the Saint Venant System Using the Entropy Viscosity Technique

# publications[].label
Invariant-domain preserving and locally mass conservative approximation of the Lagrangian hydrodynamics equations

# publications[].label
Finite volume methods on unstructured Voronoi meshes for hyperbolic conservation laws

# publications[].label
From suitable weak solutions to entropy viscosity

# publications[].label
WELL-BALANCED SECOND-ORDER FINITE ELEMENT APPROXIMATION OF THE SHALLOW WATER EQUATIONS WITH FRICTION

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
A Second Order Central Scheme for Hamilton-Jacobi Equations on Triangular Grids

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Invariant domains and first-order continuous finite element  approximation for hyperbolic systems

# publications[].label
Convergence analysis of wavelet schemes for convection-reaction equations under minimal regularity assumptions

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
The Effect of the Consistent Mass Matrix on the Maximum-Principle for Scalar Conservation Equations

# publications[].label
On convex approximation by quadratic splines

# publications[].label
Robust second-order approximation of the compressible Euler equations with an arbitrary equation of state

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Linear transport equations with discontinuous coefficients

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ENTROPY VISCOSITY FOR THE EULER EQUATIONS AND QUESTIONS REGARDING PARABOLIC REGULARIZATION

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Finite element-based invariant-domain preserving approximation of hyperbolic systems: Beyond second-order accuracy in space

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Fast algorithm for solving first-order PDES by L-1-minimization

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CALCULATION OF THE SOLUBILITY-TEMPERATURE RELATIONSHIP FOR NITROGEN IN NICKEL MELTS.

# publications[].label
Order of convergence of second order schemes based on the minmod limiter

# publications[].label
A Second Order Central Scheme for Hamilton-Jacobi Equations on Triangular Grids

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Surface Reconstruction via L 1-Minimization

# publications[].label
A SECOND-ORDER MAXIMUM PRINCIPLE PRESERVING LAGRANGE FINITE ELEMENT TECHNIQUE FOR NONLINEAR SCALAR CONSERVATION EQUATIONS

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
Second-order invariant domain preserving approximation of the compressible Navier-Stokes equations

# publications[].label
SECOND-ORDER INVARIANT DOMAIN PRESERVING APPROXIMATION OF THE EULER EQUATIONS USING CONVEX LIMITING

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
Invariant domain preserving discretization-independent schemes and   convex limiting for hyperbolic systems

# publications[].label
Weakly nonoscillatory schemes for scalar conservation laws

# publications[].label
Implementation of the entropy viscosity method with the discontinuous Galerkin method

# publications[].label
Fast estimation from above of the maximum wave speed in the Riemann problem for the Euler equations

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VISCOUS REGULARIZATION OF THE EULER EQUATIONS AND ENTROPY PRINCIPLES

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
On the implementation of a robust and efficient finite element-based parallel solver for the compressible Navier-Stokes equations

# publications[].label
Second-order invariant domain preserving ALE approximation of hyperbolic systems

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SURFACE RECONSTRUCTION AND IMAGE ENHANCEMENT VIA L-1-MINIMIZATION

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
WELL-BALANCED SECOND-ORDER APPROXIMATION OF THE SHALLOW WATER EQUATION WITH CONTINUOUS FINITE ELEMENTS

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
ERROR ESTIMATES OF A FIRST-ORDER LAGRANGE FINITE ELEMENT TECHNIQUE FOR NONLINEAR SCALAR CONSERVATION EQUATIONS

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
Positive asymptotic preserving approximation of the radiation transport  equation

# publications[].label
Activity of nitrogen and sulfur in metallic melts

# publications[].label
Hyperbolic relaxation technique for solving the dispersive  Serre-Green-Naghdi Equations with topography

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Dispersion in fatigue crack growth rate and processing of experimental data

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Hyperbolic relaxation technique for solving the dispersive Serre-Green-Naghdi equations with topography

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Linear advection with ill-posed boundary conditions via L1-minimization

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AN OPTIMAL L(1)-MINIMIZATION ALGORITHM FOR STATIONARY HAMILTON-JACOBI EQUATIONS

# publications[].label
INVARIANT DOMAINS PRESERVING ARBITRARY LAGRANGIAN EULERIAN APPROXIMATION OF HYPERBOLIC SYSTEMS WITH CONTINUOUS FINITE ELEMENTS

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
Entropy-viscosity method for the single material Euler equations in Lagrangian frame

# publications[].label
Robust second-order approximation of the compressible Euler equations  with an arbitrary equation of state

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Moduli of smoothness of splines and applications in constrained approximation

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STABILITY ANALYSIS OF EXPLICIT ENTROPY VISCOSITY METHODS FOR NON-LINEAR SCALAR CONSERVATION EQUATIONS

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First-Order Greedy Invariant-Domain Preserving Approximation for Hyperbolic Problems: Scalar Conservation Laws, and p-System

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Second-Order Invariant Domain Preserving ALE Approximation of Euler Equations

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One-sided stability and convergence of the Nessyahu-Tadmor scheme

# publications[].label
Methods for determining node location in asymptotically uniform spline approximation

# publications[].label
Nonlinear best Chebyshev approximations and splines

# publications[].label
Temperature dependence of the activity coefficient of carbon in multicomponent iron-based melts

# publications[].label
Fast estimation from above of the maximum wave speed in the Riemann  problem for the Euler equations

# publications[].label
Second-order invariant domain preserving approximation of the Euler  equations using convex limiting

# publications[].label
Linear Transport Equations with -Monotone Coefficients

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Adaptive semidiscrete central-upwind schemes for nonconvex hyperbolic conservation laws

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
MAXIMUM PRINCIPLE AND CONVERGENCE OF CENTRAL SCHEMES BASED ON SLOPE LIMITERS

# publications[].label
INVARIANT DOMAINS AND FIRST-ORDER CONTINUOUS FINITE ELEMENT APPROXIMATION FOR HYPERBOLIC SYSTEMS

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
INVARIANT DOMAIN-PRESERVING APPROXIMATIONS FOR THE EULER EQUATIONS WITH TABULATED EQUATION OF STATE

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
Entropy viscosity method for nonlinear conservation laws

# publications[].label
Entropy Viscosity and L1-based Approximations of PDEs: Exploiting Sparsity

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POSITIVE AND ASYMPTOTIC PRESERVING APPROXIMATION OF THE RADIATION TRANSPORT EQUATION

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
INVARIANT DOMAIN PRESERVING CENTRAL SCHEMES FOR NONLINEAR HYPERBOLIC SYSTEMS

# researcherOn[].label
Entropy Viscosity and L-1 Based Approximations of Pdes: Exploiting Sparsity

# researcherOn[].awardedBy.label
United States Air Force - (Arlington, Virginia, United States)

# researcherOn[].awardedBy.preferredLabel
DOD-Air Force-Office of Scientific Research

# researcherOn[].label
Robust approximation of nonlinear conservation equations

# researcherOn[].awardedBy.label
United States Army - (Washington D.C., District of Columbia, United States)

# researcherOn[].label
Finite Element Approximation of Nonlinear Systems Developing Shocks, Fronts and Interfaces

# researcherOn[].awardedBy.label
United States Army - (Washington D.C., District of Columbia, United States)

# researcherOn[].label
Robust and Accurate Approximation of Hyperbolic Systems

# researcherOn[].awardedBy.label
United States Air Force - (Arlington, Virginia, United States)

# researcherOn[].awardedBy.preferredLabel
DOD-Air Force-Office of Scientific Research

# researcherOn[].label
Robust Approximation of Nonlinear Hyperbolic Systems

# researcherOn[].awardedBy.label
United States Air Force - (Arlington, Virginia, United States)

# researcherOn[].awardedBy.preferredLabel
DOD-Air Force-Office of Scientific Research

# researcherOn[].label
High-Order Approximation Techniques for Nonlinear Hyperbolic Pdes

# researcherOn[].awardedBy.label
National Science Foundation - (Arlington, Virginia, United States)

# researcherOn[].label
High-Order Invariant Domain Preserving-Numerical Methods for Nonlinear Hyperbolic Systems-

# researcherOn[].awardedBy.label
National Science Foundation - (Arlington, Virginia, United States)

# streetAddress
Texas A&M University; Mathematics; 3368 TAMU

# etdChairOf[].label
Tomov, Vladimir (2014-05). Entropy Viscosity Method for Lagrangian Hydrodynamics and Central Schemes for Mean Field Games. Doctoral Dissertation.

# etdChairOf[].label
Mehmetoglu, Orhan (2012-08). Stability and Convergence of High Order Numerical Methods for Nonlinear Hyperbolic Conservation Laws. Doctoral Dissertation.