Stability conditions for the numerical solution of convection-dominated problems with skew-symmetric discretizations
Provides rigorous stability bounds for numerical schemes in convection-dominated PDEs, relevant to computational scientists and engineers.
The paper derives optimal stability conditions (δt ≤ C δx^α with α = 2r/(2r-1)) for skew-symmetric discretizations of convection-dominated problems, stronger than the CFL condition, and validates them numerically for nonlinear equations.
This paper presents original and close to optimal stability conditions linking the time step and the space step, stronger than the CFL criterion: $δt\leq Cδx^α$ with $α=\frac{2r}{2r-1}$, $r$ an integer, for some numerical schemes we produce, when solving convection-dominated problems. We test this condition numerically and prove that it applies to nonlinear equations under smoothness assumptions.