Related papers: High order conservative LDG-IMEX methods for the d…
The aim of this paper is to apply a high-order discontinuous-in-time scheme to second-order hyperbolic partial differential equations (PDEs). We first discretize the PDEs in time while keeping the spatial differential operators…
We present a novel quasi-conservative arbitrary high order accurate ADER discontinuous Galerkin (DG) method allowing to efficiently use a non-conservative form of the considered partial differential system, so that the governing equations…
Recently, it was discovered that the entropy-conserving/dissipative high-order split-form discontinuous Galerkin discretizations have robustness issues when trying to solve the simple density wave propagation example for the compressible…
We consider the initial/boundary value problem for a diffusion equation involving multiple time-fractional derivatives on a bounded convex polyhedral domain. We analyze a space semidiscrete scheme based on the standard Galerkin finite…
For the case of approximation of convection--diffusion equations using piecewise affine continuous finite elements a new edge-based nonlinear diffusion operator is proposed that makes the scheme satisfy a discrete maximum principle. The…
This paper presents a conservative discontinuous Galerkin method for the simulation of supercritical and transcritical real-fluid flows without phase separation. A well-known issue associated with the use of fully conservative schemes is…
In the present work, we investigate a model of the invasion of healthy tissue by cancer cells which is described by a system of nonlinear PDEs consisting of a cross-diffusion-reaction equation and two additional nonlinear ordinary…
This paper presents a fast high-order method for the solution of two-dimensional problems of scattering by penetrable inhomogeneous media, with application to high-frequency configurations containing (possibly) discontinuous refractivities.…
In this paper, we present and analyze an interior penalty discontinuous Galerkin method for the distributed elliptic optimal control problems. It is based on a reconstructed discontinuous approximation which admits arbitrarily high-order…
In this work, we propose and investigate stable high-order collocation-type discretisations of the discontinuous Galerkin method on equidistant and scattered collocation points. We do so by incorporating the concept of discrete least…
The Swift-Hohenberg equation as a central nonlinear model in modern physics has a gradient flow structure. Here we introduce fully discrete discontinuous Galerkin (DG) schemes for a class of fourth order gradient flow problems, including…
We assess the ability of three different approaches based on high-order discontinuous Galerkin methods to simulate under-resolved turbulent flows. The capabilities of the mass conserving mixed stress method as structure resolving large eddy…
The computation of the radiative transfer equation is expensive mainly due to two stiff terms: the transport term and the collision operator. The stiffness in the former comes from the fact that particles (such as photons) travels at the…
In this paper, we study numerical methods for the homogenization of linear second-order elliptic equations in nondivergence-form with periodic diffusion coefficients and large drift terms. Upon noting that the effective diffusion matrix can…
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…
Maintaining conservation laws in the fully discrete setting is critical for accurate long-time behavior of numerical simulations and requires accounting for discrete conservation properties in both space and time. This paper derives…
We derive and analyze a broad class of finite element methods for numerically simulating the stationary, low Reynolds number flow of concentrated mixtures of several distinct chemical species in a common thermodynamic phase. The underlying…
Fully implicit Runge-Kutta (IRK) methods have many desirable accuracy and stability properties as time integration schemes, but high-order IRK methods are not commonly used in practice with large-scale numerical PDEs because of the…
In this paper we want to propose practical numerical methods to solve a class of initial-boundary problem of time-space fractional convection-diffusion equations (TSFCDEs). To start with, an implicit difference method based on two-sided…
A wide variety of different (fixed-point) iterative methods for the solution of nonlinear equations exists. In this work we will revisit a unified iteration scheme in Hilbert spaces from our previous work that covers some prominent…