6,773 research outputs found
Numerical approximation of statistical solutions of scalar conservation laws
We propose efficient numerical algorithms for approximating statistical
solutions of scalar conservation laws. The proposed algorithms combine finite
volume spatio-temporal approximations with Monte Carlo and multi-level Monte
Carlo discretizations of the probability space. Both sets of methods are proved
to converge to the entropy statistical solution. We also prove that there is a
considerable gain in efficiency resulting from the multi-level Monte Carlo
method over the standard Monte Carlo method. Numerical experiments illustrating
the ability of both methods to accurately compute multi-point statistical
quantities of interest are also presented
Numerical approximation of statistical solutions of scalar conservation laws
We propose efficient numerical algorithms for approximating statistical
solutions of scalar conservation laws. The proposed algorithms combine finite
volume spatio-temporal approximations with Monte Carlo and multi-level Monte
Carlo discretizations of the probability space. Both sets of methods are proved
to converge to the entropy statistical solution. We also prove that there is a
considerable gain in efficiency resulting from the multi-level Monte Carlo
method over the standard Monte Carlo method. Numerical experiments illustrating
the ability of both methods to accurately compute multi-point statistical
quantities of interest are also presented
Towards new schemes: A Lie-group approach of the CBKDV and its derived equations
The aim of this paper is to propose methods that enable us to build new
numerical schemes, which preserve the Lie symmetries of the original
differential equations. To this purpose, the compound Burgers-Korteweg-de Vries
(\textit{CBKDV}) equation is considered. The particular case of the Burgers
equation is taken as a numerical example, and the resulting semi-invariant
scheme is exposed
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