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The RungeKutta discontinuous Galerkin method for conservation laws V: multidimensional systems
, 1997
"... This is the fifth paper in a series in which we construct and study the socalled RungeKutta Discontinuous Galerkin method for numerically solving hyperbolic conservation laws. In this paper, we extend the method to multidimensional nonlinear systems of conservation laws. The algorithms are describ ..."
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Cited by 508 (44 self)
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This is the fifth paper in a series in which we construct and study the socalled RungeKutta Discontinuous Galerkin method for numerically solving hyperbolic conservation laws. In this paper, we extend the method to multidimensional nonlinear systems of conservation laws. The algorithms
Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes
 J. COMP. PHYS
, 1981
"... Several numerical schemes for the solution of hyperbolic conservation laws are based on exploiting the information obtained by considering a sequence of Riemann problems. It is argued that in existing schemes much of this information is degraded, and that only certain features of the exact solution ..."
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Cited by 1010 (2 self)
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Several numerical schemes for the solution of hyperbolic conservation laws are based on exploiting the information obtained by considering a sequence of Riemann problems. It is argued that in existing schemes much of this information is degraded, and that only certain features of the exact solution
Fronts propagating with curvature dependent speed: algorithms based on Hamilton–Jacobi formulations
, 1988
"... We devise new numerical algorithms, called PSC algorithms, for following fronts propagating with curvaturedependent speed. The speed may be an arbitrary function of curvature, and the front also can be passively advected by an underlying flow. These algorithms approximate the equations of motion, w ..."
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Cited by 1183 (60 self)
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, which resemble HamiltonJacobi equations with parabolic righthand sides, by using techniques from hyperbolic conservation laws. Nonoscillatory schemes of various orders of accuracy are used to solve the equations, providing methods that accurately capture the formation of sharp gradients and cusps
A Fast Marching Level Set Method for Monotonically Advancing Fronts
 PROC. NAT. ACAD. SCI
, 1995
"... We present a fast marching level set method for monotonically advancing fronts, which leads to an extremely fast scheme for solving the Eikonal equation. Level set methods are numerical techniques for computing the position of propagating fronts. They rely on an initial value partial differential eq ..."
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Cited by 630 (24 self)
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equation for a propagating level set function, and use techniques borrowed from hyperbolic conservation laws. Topological changes, corner and cusp development, and accurate determination of geometric properties such as curvature and normal direction are naturally obtained in this setting. In this paper, we
Efficient Implementation of Weighted ENO Schemes
, 1995
"... In this paper, we further analyze, test, modify and improve the high order WENO (weighted essentially nonoscillatory) finite difference schemes of Liu, Osher and Chan [9]. It was shown by Liu et al. that WENO schemes constructed from the r th order (in L¹ norm) ENO schemes are (r +1) th order accur ..."
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Cited by 412 (38 self)
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waves. We also prove that, for conservation laws with smooth solutions, all WENO schemes are convergent. Many numerical tests, including the 1D steady state nozzle flow problem and 2D shock entropy waveinteraction problem, are presented to demonstrate the remarkable capability of the WENO schemes
The laws of emotion
, 2007
"... ABSTRACT: It is argued that emotions are lawful phenomena and thus can be described in terms of a set of laws of emotion. These laws result from the operation of emotion mechanisms that are accessible to intentional control to only a limited extent. The law of situational meaning, the law of concer ..."
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Cited by 331 (4 self)
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of concern, the law of reality, the laws of change, habituation and comparative f eling, and the law of hedonic asymmetry are proposed to describe motion elicitation; the law of conservation of emotional momentum formulates emotion persistence, " the law of closure expresses the modularity of emotion
Nonoscillatory central differencing for hyperbolic conservation laws
 J. COMPUT. PHYS
, 1990
"... Many of the recently developed highresolution schemes for hyperbolic conservation laws are based on upwind differencing. The building block of these schemes is the averaging of an approximate Godunov solver; its time consuming part involves the fieldbyfield decomposition which is required in orde ..."
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Cited by 298 (25 self)
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Many of the recently developed highresolution schemes for hyperbolic conservation laws are based on upwind differencing. The building block of these schemes is the averaging of an approximate Godunov solver; its time consuming part involves the fieldbyfield decomposition which is required
Conservation laws for equations related to soil water equations
 Math. Probl. Engin
"... We obtain all nontrivial conservation laws for a class of (2 + 1) nonlinear evolution partial differential equations which are related to the soil water equations. It is also pointed out that nontrivial conservation laws exist for certain classes of equations which admit point symmetries. Moreover, ..."
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Cited by 1 (0 self)
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We obtain all nontrivial conservation laws for a class of (2 + 1) nonlinear evolution partial differential equations which are related to the soil water equations. It is also pointed out that nontrivial conservation laws exist for certain classes of equations which admit point symmetries. Moreover
Conservation laws in elasticity. II. Linear homogeneous isotropic elastostatics
 Arch. Rational Mech. Anal
, 1984
"... In 1956 ESHELBY, [5], introduced his celebrated energymomentum tensor in his study of lattice defects. This tensor had the useful property of providing nontrivial pathindependent integrals for the equations of finite elasticity, or, in other words, providing densities of nontrivial conservation la ..."
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Cited by 22 (8 self)
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In 1956 ESHELBY, [5], introduced his celebrated energymomentum tensor in his study of lattice defects. This tensor had the useful property of providing nontrivial pathindependent integrals for the equations of finite elasticity, or, in other words, providing densities of nontrivial conservation
Symmetries and Conservation Laws for Some Compacton Equation
"... We consider some equations with compacton solutions and nonlinear dispersion from the point of view of Lie classical reductions. The reduced ordinary differential equations are suitable for qualitative analysis and their dynamical behaviour is described. We derive by using the multipliers method so ..."
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