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Creators/Authors contains: "Popov, Bojan"

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  1. ; ; ; (, Computer methods in applied mechanics and engineering)
    In this paper we construct an explicit approximation for the Lagrangian hydrodynamics equations equipped with an arbitrary equation of state. The approximation of the state variable is done with piecewise constant finite elements and the approximation of the mesh motion is done with higher-order continuous finite elements. The method is invariant-domain preserving and locally mass conservative. The purpose of this method is to be used in combination with higher-order methods to make them invariant domain preserving as well. 
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    Free, publicly-accessible full text available June 1, 2026
  2. ; ; ; ; (, Journal of Scientific Computing)
    The paper focuses on first-order invariant-domain preserving approximations of hyperbolic systems. We propose a new way to estimate the artificial viscosity that has to be added to make explicit, conservative, consistent numerical methods invariant-domain preserving and entropy inequality compliant. Instead of computing an upper bound on the maximum wave speed in Riemann problems, we estimate a minimum wave speed in the said Riemann problems such that the approximation satisfies predefined invariant-domain properties and predefined entropy inequalities. This technique eliminates non-essential fast waves from the construction of the artificial viscosity, while preserving pre-assigned invariant-domain properties and entropy inequalities. 
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  3. ; ; (, Computer Methods in Applied Mechanics and Engineering)
    This paper proposes an invariant-domain preserving approximation technique for nonlinear conservation systems that is high-order accurate in space and time. The algorithm mixes a high order finite element method with an invariant-domain preserving low-order method that uses the closest neighbor stencil. The construction of the flux of the low-order method is based on an idea from Abgrall et al. (2017). The mass flux of the low-order and the high-order methods are identical on each finite element cell. This allows for mass preserving and invariant-domain preserving limiting. 
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  4. ; ; (, Communications on Applied Mathematics and Computation)
    Abstract An invariant domain preserving arbitrary Lagrangian-Eulerian method for solving non-linear hyperbolic systems is developed. The numerical scheme is explicit in time and the approximation in space is done with continuous finite elements. The method is made invariant domain preserving for the Euler equations using convex limiting and is tested on various benchmarks. 
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  5. ; ; ; ; (, Journal of Computational Physics)
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  6. ; ; ; (, Water Waves)
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  7. ; ; (, SIAM Journal on Scientific Computing)
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  8. ; ; ; ; (, Computer Methods in Applied Mechanics and Engineering)
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  9. ; ; ; (, Computer Methods in Applied Mechanics and Engineering)
    null (Ed.)
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