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Equations of state (EOS) are considered as solutions of "conservation equations" or of their corresponding first-order partial differential equations.
It is well known that the spectral solutions of conservation laws have the attractive distinguishing property of infinite-order convergence (also called spectral accuracy) when they are smooth (e.g., [C. Canuto, M.Y.
This work introduces a novel discontinuity-tracking framework for resolving discontinuous solutions of conservation laws with high-order numerical discretizations that support inter-element solution discontinuities, such as discontinuous Galerkin or finite volume methods.
These programmes have been celebrated and critiqued for attempting 'win-win' solutions of conservation and development.
This approach was introduced by Chen and Frid [10] to study the asymptotic behavior of the entropy solutions of conservation laws.
Solutions of conservation laws satisfy the monotonicity property: the number of local extrema is a non-increasing function of time, and local maximum/minimum values decrease/increase monotonically in time.
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The combination of these produces a quick algorithm for the solution of conservation laws.
We consider finite volume methods for the numerical solution of conservation laws.
A new class of high-order monotonicity-preserving schemes for the numerical solution of conservation laws is presented.
The numerical solution of conservation laws by minimizing the residuals of an overdetermined set of discrete equations is studied.
The derivation of the finite element formulation is based on the weak solution of conservation of mass and linear momentum and on the Galerkin method.
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