Scalar conservation laws with white noise initial data
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DOI: 10.1007/s00440-021-01083-z
Abstract: The statistical description of the scalar conservation law of the form $\rho_t=H(\rho)_x$ with $H: \mathbb{R} \rightarrow \mathbb{R}$ a smooth convex function has been an object of interest when the initial profile $\rho(\cdot,0)$ is random. The… read more here.
Keywords: conservation laws; laws white; scalar conservation; white noise ... See more keywords
A posteriori error analysis and adaptive non-intrusive numerical schemes for systems of random conservation laws
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DOI: 10.1007/s10543-019-00794-z
Abstract: This article considers one-dimensional random systems of hyperbolic conservation laws. Existence and uniqueness of random entropy admissible solutions for initial value problems of conservation laws, which involve random initial data and random flux functions, are… read more here.
Keywords: error analysis; non intrusive; random; conservation laws ... See more keywords
Conservation of Energy: Missing Features in Its Nature and Justification and Why They Matter
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DOI: 10.1007/s10699-020-09657-1
Abstract: Misconceptions about energy conservation abound due to the gap between physics and secondary school chemistry. This paper surveys this difference and its relevance to the 1690s–2010s Leibnizian argument that mind-body interaction is impossible due to… read more here.
Keywords: energy; physics; conservation; energy missing ... See more keywords
Performance and Scalability Improvements for Discontinuous Galerkin Solutions to Conservation Laws on Unstructured Grids
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DOI: 10.1007/s10915-016-0249-y
Abstract: This paper presents a computational framework developed to improve both the serial and parallel performance of two dimensional, unstructured, discontinuous Galerkin (DG) solutions to hyperbolic conservation laws. The coding techniques employed factor in advancements trending… read more here.
Keywords: galerkin solutions; discontinuous galerkin; performance; conservation laws ... See more keywords
An Approximate Lax–Wendroff-Type Procedure for High Order Accurate Schemes for Hyperbolic Conservation Laws
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DOI: 10.1007/s10915-016-0298-2
Abstract: A high order time stepping applied to spatial discretizations provided by the method of lines for hyperbolic conservations laws is presented. This procedure is related to the one proposed in Qiu and Shu (SIAM J… read more here.
Keywords: procedure; lax wendroff; high order; conservation laws ... See more keywords
Enhanced Robustness of the Hybrid Compact-WENO Finite Difference Scheme for Hyperbolic Conservation Laws with Multi-resolution Analysis and Tukey’s Boxplot Method
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DOI: 10.1007/s10915-017-0465-0
Abstract: The high order shock detection algorithm employing the high order multi-resolution (MR) analysis (Harten in J Comput Phys 49:357–393, 1983) for identifying the smooth and non-smooth stencils has been employed extensively in the hybrid schemes,… read more here.
Keywords: analysis; scheme; detection algorithm; conservation laws ... See more keywords
Numerical Analysis for Conservation Laws Using $$l_1$$l1 Minimization
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DOI: 10.1007/s10915-019-00982-7
Abstract: This paper develops and analyzes a new numerical scheme for solving hyperbolic conservation laws that combines the Lax Wendroff method with $$l_1$$l1 regularization. While prior investigations constructed similar algorithms, the method developed here adds a… read more here.
Keywords: using minimization; numerical analysis; conservation; analysis conservation ... See more keywords
Duality for systems of conservation laws
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DOI: 10.1007/s11005-019-01253-0
Abstract: For one-dimensional systems of conservation laws admitting two additional conservation laws, we assign a ruled hypersurface of codimension two in projective space. We call two such systems dual if the corresponding ruled hypersurfaces are dual.… read more here.
Keywords: systems conservation; conservation; duality systems; conservation laws ... See more keywords
Optimal system, group invariant solutions and conservation laws of the CGKP equation
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DOI: 10.1007/s11071-017-3392-6
Abstract: In this paper, the (2 + 1)-dimensional cubic generalized Kadomtsev–Petviashvili (CGKP) equation that is derived from the Maxwell–Bloch equations is investigated. By means of Lie symmetry analysis method, we obtain the Lie point symmetries for the equation… read more here.
Keywords: group invariant; invariant solutions; system; optimal system ... See more keywords
The dispersionless Veselov–Novikov equation: symmetries, exact solutions, and conservation laws
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DOI: 10.1007/s13324-021-00563-8
Abstract: We study symmetries, invariant solutions, and conservation laws for the dispersionless Veselov–Novikov equation. The emphasis is placed on cases when the odes involved in description of the invariant solutions are integrable by quadratures. Then we… read more here.
Keywords: dispersionless veselov; novikov equation; solutions conservation; conservation ... See more keywords
Convergence of the Finite Volume method for scalar conservation laws with multiplicative noise: an approach by kinetic formulation
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DOI: 10.1007/s40072-019-00146-6
Abstract: Under a standard CFL condition, we prove the convergence of the explicit-in-time Finite Volume method with monotone fluxes for the approximation of scalar first-order conservation laws with multiplicative, compactly supported noise. In Dotti and Vovelle… read more here.
Keywords: formulation; convergence; kinetic formulation; method ... See more keywords