The existence of discrete shock profiles for difference schemes approximating a system of conservation laws is the major topic studied in this paper. The basic theorem established here applies to first‐order accurate difference schemes; for weak shocks, this theorem provides necessary and sufficient conditions involving the truncation error of the linearized scheme which guarantee entropy satisfying or entropy violating discrete shock profiles. Several explicit difference schemes are used as examples illustrating the interplay between the entropy condition, monotonicity, and linearized stability. Entropy violating stationary shocks for second‐order accurate Lax‐Wendroff schemes approximating systems are also constructed. The only tools used in the proofs are local analysis and the center manifold theorem.
ASJC Scopus subject areas
- Applied Mathematics