Structure-Preserving Function Approximation via Convex Optimization

TL;DR: In this article , the authors proposed a hyperbolicity-preserving stochastic Galerkin formulation by carefully selecting the polynomial chaos approximations to the nonlinear terms in the shallow water equations.

TL;DR: In this paper, the authors present a new framework that enforces via optimization such structure on approximations and is simultaneously norm-preserving, which results in a conceptually simple convex optimization problem on the sphere.

TL;DR: In this paper , the authors present a new framework that enforces via optimization such structure on approximations and is simultaneously norm-preserving, which results in a conceptually simple convex optimization problem on the sphere.

TL;DR: This work proposes an innovative filter based on convex optimization to deal with the inconsistencies observed in polynomial-based simulations and presents the construction and application of a structure-preserving filter with a focus on multidimensional PDEs.

TL;DR: This paper treats numerical methods based on either discretization or local reduction with the emphasis on the design of superlinearly convergent (SQP-type) methods.

TL;DR: Various methods of finding points from the intersection of sets, using projection on to a separate set as an elementary operation are considered, and the strong convergence of the sequences obtained is proved.

TL;DR: This paper presents a simpler implementation of genuinely high-order accurate finite volume and discontinuous Galerkin schemes satisfying a strict maximum principle for scalar conservation laws, which will result in a significant reduction of computational cost especially for weighted essentially non-oscillatory finite-volume schemes.

TL;DR: In this paper, the method of successive approximation is applied to the problem of obtaining points of minimum distance on two convex sets and it is shown that every fixed point of Q is a point of Ki closest to K2, and that the fixed points of Q may be obtained by iteration of Q when one of the sets is compact or when both are polytopes in E