Related papers: A skeletal high-order structure preserving scheme …
In this paper, we present an interior penalty discontinuous Galerkin finite element scheme for solving diffusion problems with strong anisotropy arising in magnetized plasmas for fusion applications. We demonstrate the accuracy produced by…
We design, analyse and implement an arbitrary order scheme applicable to generic meshes for a coupled elliptic-parabolic PDE system describing miscible displacement in porous media. The discretisation is based on several adaptations of the…
In this paper, a novel high-order, mass and energy-conserving scheme is proposed for the regularized logarithmic Schr\"{o}dinger equation(RLogSE). Based on the idea of the supplementary variable method (SVM), we firstly reformulate the…
In this article we introduce an asymptotic preserving scheme designed to compute the solution of a two dimensional elliptic equation presenting large anisotropies. We focus on an anisotropy aligned with one direction, the dominant part of…
We present a high-order conservative, positivity-preserving, and non-oscillatory scheme for solving the Vlasov equation. The scheme attains formal fifth-order accuracy through a convex combination of positive and non-oscillatory polynomials…
In this work, we develop a new hydrostatic reconstruction procedure to construct well-balanced schemes for one and multilayer shallow water flows, including wetting and drying. Initially, we derive the method for a path-conservative finite…
Non-local systems of conservation laws play a crucial role in modeling flow mechanisms across various scenarios. The well-posedness of such problems is typically established by demonstrating the convergence of robust first-order schemes.…
This paper is concerned with moving mesh finite difference solution of partial differential equations. It is known that mesh movement introduces an extra convection term and its numerical treatment has a significant impact on the stability…
We study a family of structure-preserving deterministic numerical schemes for Lindblad equations. This family of schemes has a simple form and can systemically achieve arbitrary high-order accuracy in theory. Moreover, these schemes can…
We present a forward semi-Lagrangian numerical method for systems of transport equations able to advect smooth and discontinuous fields with high-order accuracy. The numerical scheme is composed of an integration of the transport equations…
In this paper, we design a novel class of arbitrarily high-order structure-preserving numerical schemes for the time-dependent Gross-Pitaevskii equation with angular momentum rotation in three dimensions. Based on the idea of the scalar…
In this study, we investigate the Shallow Water Equations incorporating source terms accounting for Manning friction and a non-flat bottom topology. Our primary focus is on developing and validating numerical schemes that serve a dual…
Different relaxation approximations to partial differential equations, including conservation laws, Hamilton-Jacobi equations, convection-diffusion problems, gas dynamics problems, have been recently proposed. The present paper focuses onto…
We propose a high-order finite element method for linear fourth-order elliptic problems that is both nodally bound-preserving and mass-conservative, based on a variational inequality formulation. The method admits an equivalent strictly…
We propose a second order finite volume scheme for nonlinear degenerate parabolic equations. For some of these models (porous media equation, drift-diffusion system for semiconductors, ...) it has been proved that the transient solution…
Preserving scalar boundedness is important for numerical schemes used in turbulent compressible multi-component flow simulations to prevent unphysical results and unstable simulations. However, ensuring scalar boundedness for high-order,…
Several relaxation approximations to partial differential equations have been recently proposed. Examples include conservation laws, Hamilton-Jacobi equations, convection-diffusion problems, gas dynamics problems. The present paper focuses…
This paper is devoted to the analysis of a numerical scheme for the coagulation and fragmentation equation with diffusion in space. A finite volume scheme is developed, based on a conservative formulation of the space nonhomogeneous…
In this paper, we develop a family of high order asymptotic preserving schemes for some discrete-velocity kinetic equations under a diffusive scaling, that in the asymptotic limit lead to macroscopic models such as the heat equation, the…
A high-order well-balanced scheme for the Euler equations with gravitation is presented. The scheme is able to preserve a spatially high-order accurate discrete representation of a large class of hydrostatic equilibria. It is based on a…