Communications in Mathematical Sciences
Volume 14 (2016)
A numerical method for the computation of tangent vectors to $2 \times 2$ hyperbolic systems of conservation laws
Pages: 683 – 704
We are interested in the development of a numerical method for solving optimal control problems governed by hyperbolic systems of conservation laws. The main difficulty of computing the derivative in the case of shock waves is resolved in the presented scheme. Our approach is based on a combination of a relaxation approach in combination with a numerical scheme to resolve the evolution of the tangent vectors. Numerical results for optimal control problems are presented.
conservation laws, optimization, tangent vectors
2010 Mathematics Subject Classification
35L65, 49K20, 49K40