Reduced basis techniques for nonlinear conservation laws

Keywords

Advanced Numerical Methods for Scientific Computing
Code:
32/2013
Title:
Reduced basis techniques for nonlinear conservation laws
Date:
Friday 16th August 2013
Author(s):
Taddei, T.; Perotto, S.; Quarteroni, A.
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Abstract:
In this paper we present a new reduced basis technique for parametrized nonlinear scalar conservation laws in presence of shocks. The essential ingredients are an efficient algorithm to approximate the shock curve, a procedure to detect the smooth components of the solution at the two sides of the shock, and a suitable interpolation strategy to reconstruct such smooth components during the online stage. The approach we propose is based on some theoretical properties of the solution to the problem. Some numerical examples prove the effectiveness of the proposed strategy.
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