Related papers: All-speed numerical methods for the Euler equation…
We focus here on a class of fourth-order parabolic equations that can be written as a system of second-order equations by introducing an auxiliary variable. We design a novel second-order fully discrete mixed finite element method to…
A numerical method for approximating weak solutions of an aggregation equation with degenerate diffusion is introduced. The numerical method consists of a stabilized finite element method together with a mass lumping technique and an extra…
Numerical methods for the Euler equations with a singular source are discussed in this paper. The stationary discontinuity induced by the singular source and its coupling with the convection of fluid presents challenges to numerical…
In this work we propose a nonlinear stabilization technique for convection-diffusion-reaction and pure transport problems discretized with space-time isogeometric analysis. The stabilization is based on a graph-theoretic artificial…
This paper extends the high-order entropy stable (ES) adaptive moving mesh finite difference schemes developed in [14] to the two- and three-dimensional (multi-component) compressible Euler equations with the stiffened equation of state.…
This paper proposes a numerical method based on the Adomian decomposition approach for the time discretization, applied to Euler equations. A recursive property is demonstrated that allows to formulate the method in an appropriate and…
We present a novel staggered semi-implicit hybrid FV/FE method for the numerical solution of the shallow water equations at all Froude numbers on unstructured meshes. A semi-discretization in time of the conservative Saint-Venant equations…
We present a novel structure-preserving semi-implicit finite volume method on vertex-based staggered meshes for the compatible discretization of first order systems of time-dependent partial differential equations (PDEs). The method…
The Euler scheme is up to date the most important numerical method for ordinary differential inclusions, because the use of the available higher-order methods is prohibited by their enormous complexity after spatial discretization.…
When evolving in time the solution of a hyperbolic partial differential equation, it is often desirable to use high order strong stability preserving (SSP) time discretizations. These time discretizations preserve the monotonicity…
We present a novel framework based on semi-bounded spatial operators for analyzing and discretizing initial boundary value problems on moving and deforming domains. This development extends an existing framework for well-posed problems and…
In Becker and Jentzen (2019) and Becker et al. (2017), an explicit temporal semi-discretization scheme and a space-time full-discretization scheme were, respectively, introduced and analyzed for the additive noise-driven stochastic…
In this paper, we analyze a semi-discrete finite volume scheme for the three-dimensional barotropic compressible Euler equations driven by a multiplicative Brownian noise. We derive necessary a priori estimates for numerical approximations,…
In contrast to the prevailing view in the literature, it is shown that even extremely stiff sets of ordinary differential equations may be solved efficiently by explicit methods if limiting algebraic solutions are used to stabilize the…
Within this paper, we introduce partially and fully decoupled time stepping schemes for linear thermo-poroelasticity. This means that the mechanics, heat, and flow equations can be solved sequentially. We provide sufficient conditions on…
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…
We investigate the temporal accuracy of two generalized-$\alpha$ schemes for the incompressible Navier-Stokes equations. The conventional approach treats the pressure with the backward Euler method while discretizing the remainder of the…
Simple and robust algorithms are developed for compressible Euler equations with the stiffened gas equation of state (EOS), representing gaseous mixtures in thermal equilibrium and without chemical reactions. These algorithms use a fully…
This report presents a low computational and cognitive complexity, stable, time accurate and adaptive method for the Navier-Stokes equations. The improved method requires a minimally intrusive modification to an existing program based on…
In this paper we propose a novel arbitrary high order accurate semi-implicit space-time discontinuous Galerkin method for the solution of the two dimensional incompressible Navier-Stokes equations on staggered unstructured triangular…