Showing papers on "L-stability published in 2021"
TL;DR: In this paper, the authors studied local stability of a parametric optimal control problem governed by semilinear elliptic equations with mixed pointwise constraints and showed that if the unperturbed problem satisfies the strictly nonnegative second-order optimality conditions, then the solution map is upper Holder continuous in the constant norm of the control variable.
Abstract: This paper studies local stability of a parametric optimal control problem governed by semilinear elliptic equations with mixed pointwise constraints. We show that if the unperturbed problem satisfies the strictly nonnegative second-order optimality conditions, then the solution map is upper Holder continuous in $$L^\infty $$
-norm of control variable.
7 citations
01 Jan 2021
TL;DR: In this paper, a convex combination between a first-order and a class of second-order IMEX schemes is proposed for a scalar hyperbolic multi-scale equation.
Abstract: We present a framework to build high-accuracy IMEX schemes that fulfill the maximum principle, applied to a scalar hyperbolic multi-scale equation. Motivated by the findings in [5] that implicit R-K schemes are not \(L^\infty \)-stable, our scheme, for which we can prove the \(L^\infty \) stability, is based on a convex combination between a first-order and a class of second-order IMEX schemes. We numerically demonstrate the advantages of our scheme, especially for discontinuous problems, and give a MOOD procedure to increase the precision.
1 citations