Related papers: High order numerical methods for networks of hyper…
In this paper we present a family of high order cut finite element methods with bound preserving properties for hyperbolic conservation laws in one space dimension. The methods are based on the discontinuous Galerkin framework and use a…
The paper develops high-order accurate physical-constraints-preserving finite difference WENO schemes for special relativistic hydrodynamical (RHD) equations, built on the local Lax-Friedrich splitting, the WENO reconstruction, the…
High order energy-preserving methods for Hamiltonian systems are presented. For this aim, an energy-preserving condition of continuous stage Runge--Kutta methods is proved. Order conditions are simplified and parallelizable conditions are…
In this paper we present an approach to approximate numerically the solution of coupled hyperbolic conservation laws. The coupling is achieved through a fixed interface, in which interface conditions are linking the traces of both sides.…
High-order implicit shock tracking (fitting) is a class of high-order, optimization-based numerical methods to approximate solutions of conservation laws with non-smooth features by aligning elements of the computational mesh with…
This paper presents the design and analysis of a Hybrid High-Order (HHO) approximation for a distributed optimal control problem governed by the Poisson equation. We propose three distinct schemes to address unconstrained control problems…
In this work, high-order discrete well-balanced methods for one-dimensional hyperbolic systems of balance laws are proposed. We aim to construct a method whose discrete steady states correspond to solutions of arbitrary high-order ODE…
It is well known, thanks to Lax-Wendroff theorem, that the local conservation of a numerical scheme for a conservative hyperbolic system is a simple and systematic way to guarantee that, if stable, a scheme will provide a sequence of…
We introduce novel high order well-balanced finite volume methods for the full compressible Euler system with gravity source term. They require no a priori knowledge of the hydrostatic solution which is to be well-balanced and are not…
In this paper we present a class of high order accurate cell-centered Arbitrary-Eulerian-Lagrangian (ALE) one-step ADER-WENO finite volume schemes for the solution of nonlinear hyperbolic conservation laws on two-dimensional unstructured…
We introduce a new scheme adaption strategy for one- and two-dimensional hyperbolic systems of conservation laws. The proposed approach builds upon the adaptive framework introduced in [S. Chu, A. Kurganov, and I. Menshov, Appl. Numer.…
We revisit the traditional upwind schemes for linear conservation laws in the viewpoint of jump processes, allowing studying upwind schemes using probabilistic tools. In particular, for Fokker-Planck equations on $\mathbb{R}$, in the case…
A novel numerical scheme to solve coupled systems of conservation laws is introduced. The scheme is derived based on a relaxation approach and does not require information on the Lax curves of the coupled systems, which simplifies the…
High-order methods are well-suited for the numerical simulation of complex compressible turbulent flows, but require additional stabilization techniques to capture instabilities arising from the underlying non-linear hyperbolic equations.…
We derive a new methodology for the construction of high order integrators for sampling the invariant measure of ergodic stochastic differential equations with dynamics constrained on a manifold. We obtain the order conditions for sampling…
In this paper we present a general procedure for designing higher strong order methods for It\^o stochastic differential equations on matrix Lie groups and illustrate this strategy with two novel schemes that have a strong convergence order…
In this work, we present a family of time and space high order finite volume schemes for the solution of the full Boltzmann equation. The velocity space is approximated by using a discrete ordinate approach while the collisional integral is…
We present THC: a new high-order flux-vector-splitting code for Newtonian and special-relativistic hydrodynamics designed for direct numerical simulations of turbulent flows. Our code implements a variety of different reconstruction…
We investigate a high-order, fully explicit, asymptotic-preserving scheme for a kinetic equation with linear relaxation, both in the hydrodynamic and diffusive scalings in which a hyperbolic, resp. parabolic, limiting equation exists. The…
In this paper, high order well-balanced finite difference weighted essentially non-oscillatory methods to solve general systems of balance laws are presented. Two different families are introduced: while the methods in the first one…