Related papers: A Broad Class of Conservative Numerical Methods fo…
The aim of this paper is the derivation of structure preserving schemes for the solution of the EPDiff equation, with particular emphasis on the two dimensional case. We develop three different schemes based on the Discrete Variational…
We consider a fully discrete loosely coupled scheme for incompressible fluid-structure interaction based on the time semi-discrete splitting method introduced in {\emph{[Burman, Durst \& Guzm\'an, arXiv:1911.06760]}}. The splittling method…
In this paper we propose optimisation methods for variational regularisation problems based on discretising the inverse scale space flow with discrete gradient methods. Inverse scale space flow generalises gradient flows by incorporating a…
A dispersive wave hydro-sediment-morphodynamic model developed by complementing the shallow water hydro-sediment-morphodynamic (SHSM) equations with the dispersive term from the Green-Naghdi equations is presented. A numerical solution…
There are several well-established approaches to constructing finite difference schemes that preserve global invariants of a given partial differential equation. However, few of these methods preserve more than one conservation law locally.…
We consider entropy conservative and dissipative discretizations of nonlinear conservation laws with implicit time discretizations and investigate the influence of iterative methods used to solve the arising nonlinear equations. We show…
In this paper we analyze the weighted essentially non-oscillatory (WENO) schemes in the finite volume framework by examining the first step of the explicit third-order total variation diminishing Runge-Kutta method. The rationale for the…
We present a class of new explicit and stable numerical algorithms to solve the spatially discretized linear heat or diffusion equation. After discretizing the space and the time variables like conventional finite difference methods, we do…
We study the conservation properties of the Hermite-discontinuous Galerkin (Hermite-DG) approximation of the Vlasov-Maxwell equations. In this semi-discrete formulation, the total mass is preserved independently for every plasma species.…
This work outlines a time-domain numerical integration technique for linear hyperbolic partial differential equations sourced by distributions (Dirac $\delta$-functions and their derivatives). Such problems arise when studying binary black…
We consider acoustic scattering in heterogeneous media with piecewise constant wave number. The discretization is carried out using a Galerkin boundary element method in space and Runge-Kutta convolution quadrature in time. We prove…
We consider model order reduction of parameterized Hamiltonian systems describing nondissipative phenomena, like wave-type and transport dominated problems. The development of reduced basis methods for such models is challenged by two main…
This paper is concerned with a few novel RBF-based numerical schemes discretizing partial differential equations. For boundary-type methods, we derive the indirect and direct symmetric boundary knot methods (BKM). The resulting…
It is difficult to design high order numerical schemes which could preserve both the maximum bound property (MBP) and energy dissipation law for certain phase field equations. Strong stability preserving (SSP) Runge-Kutta methods have been…
We propose a class of semi-Lagrangian methods of high approximation order in space and time, based on spectral element space discretizations and exponential integrators of Runge-Kutta type. We discuss the extension of these methods to the…
This paper deals with the numerical solution of conservation laws in the two dimensional case using a novel compact implicit time discretization that enables applications of fast algebraic solvers. We present details for the second order…
We consider flux-corrected finite element discretizations of 3D convection-dominated transport problems and assess the computational efficiency of algorithms based on such approximations. The methods under investigation include…
In this paper, we study the large--time behavior of a numerical scheme discretizing drift-- diffusion systems for semiconductors. The numerical method is finite volume in space, implicit in time, and the numerical fluxes are a…
This paper aims at developing exactly energy-conservative and structure-preserving finite volume schemes for the discretisation of first-order symmetric-hyperbolic and thermodynamically compatible (SHTC) systems of partial differential…
We introduce discontinuous spectral-element methods of arbitrary order that are well balanced, conservative of mass, and conservative or dissipative of total energy (i.e., a mathematical entropy function) for a covariant flux formulation of…