Reduced basis techniques for nonlinear conservation laws
نویسندگان
چکیده
منابع مشابه
Reduced Basis Method for Explicit Finite Volume Approximations of Nonlinear Conservation Laws
The numerical solution of parametrized partial differential equations (P2DEs ) can be a very time-consuming task if many parameter constellations have to be simulated by high-resolution schemes. Such scenarios may occur in parameter studies, optimization, control, inverse problems or statistical analysis of a given P2DE . Reduced Basis (RB) methods allow to produce fast reduced models that are ...
متن کاملA reduced stability condition for nonlinear relaxation to conservation laws
We consider multidimensional hyperbolic systems of conservation laws with relaxation, together with their associated limit systems. A strong stability condition for such asymptotics has been introduced by Chen, Levermore, Liu in Comm. Pure Appl. Math. 47, 787-830, namely the existence of an entropy extension. We propose here a new stability condition, the reduced stability condition, which is w...
متن کاملA total variation diminishing high resolution scheme for nonlinear conservation laws
In this paper we propose a novel high resolution scheme for scalar nonlinear hyperbolic conservation laws. The aim of high resolution schemes is to provide at least second order accuracy in smooth regions and produce sharp solutions near the discontinuities. We prove that the proposed scheme that is derived by utilizing an appropriate flux limiter is nonlinear stable in the sense of total varia...
متن کاملEntropy viscosity method for nonlinear conservation laws
A new class of high-order numerical methods for approximating nonlinear conservation laws is described (entropy viscosity method). The novelty is that a nonlinear viscosity based on the local size of an entropy production is added to the numerical discretization at hand. This new approach does not use any flux or slope limiters, applies to equations or systems supplemented with one or more entr...
متن کاملConservation laws for nonlinear telegraph equations
A complete conservation law classification is given for nonlinear telegraph (NLT) systems with respect to multipliers that are functions of independent and dependent variables. It turns out that a very large class of NLT systems admits four nontrivial local conservation laws. The results of this work are summarized in tables which display all multipliers, fluxes and densities for the correspond...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: ESAIM: Mathematical Modelling and Numerical Analysis
سال: 2015
ISSN: 0764-583X,1290-3841
DOI: 10.1051/m2an/2014054