Related papers: A Characteristic Mapping Method with Source Terms:…
We extend the recently introduced explicit divergence-free DG scheme for incompressible hydrodynamics [arXiv:1808.04669]. to the incompressible magnetohydrodynamics (MHD). A globally divergence-free finite element space is used for both the…
This is the second component of a two-part paper dealing with a unification of characteristic mode decomposition. This second part addresses modal tracking and losses and presents several numerical examples for both surface- and…
This paper proposes a novel first-order and a novel second-order fully discrete virtual element schemes based on the scalar auxiliary variable method for the three dimensional inductionless magnetohydrodynamics problem. The backward Eular…
A material-based, i.e., Lagrangian, methodology for exact integration of flux by volume-preserving flows through a surface has been developed recently in [Karrasch, SIAM J. Appl. Math., 76 (2016), pp. 1178-1190]. In the present paper, we…
This paper develops a fully discrete modified characteristic finite element method for a coupled system consisting of the fully nonlinear Monge-Amp\'ere equation and a transport equation. The system is the Eulerian formulation in the dual…
An efficient method for solving large nonlinear problems combines Newton solvers and Domain Decomposition Methods (DDM). In the DDM framework, the boundary conditions can be chosen to be primal, dual or mixed. The mixed approach presents…
We construct and analyze a model of the relativistic steady-state magnetohydrodynamic (MHD) rarefaction that is induced when a planar symmetric flow (with one ignorable Cartesian coordinate) propagates under a steep drop of the external…
The formalism of frozen-in vortex lines for two-dimensional (2D) flows in ideal incompressible electron magnetohydrodynamics (EMHD) is formulated. A localized approximation for nonlinear dynamics of two close sheets of the generalized…
We introduce a new hybridized discontinuous Galerkin method for the incompressible magnetohydrodynamics equations. If particular velocity, pressure, magnetic field, and magnetic pressure spaces are employed for both element and trace…
We present and analyze a linearized finite element method (FEM) for the dynamical incompressible magnetohydrodynamics (MHD) equations. The finite element approximation is based on mixed conforming elements, where Taylor--Hood type elements…
Modern simulation codes for general relativistic ideal magnetohydrodynamics are all facing a long standing technical problem given by the need to recover fundamental variables from those variables that are evolved in time. In the…
This paper focuses on an optimal error analysis of a fully discrete finite element scheme for the Cahn--Hilliard--magnetohydrodynamic (CH-MHD) system. The method use the standard inf-sup stable Taylor--Hood/MINI elements to solve the…
We present a new numerical tool for solving the special relativistic ideal MHD equations that is based on the combination of the following three key features: (i) a one-step ADER discontinuous Galerkin (DG) scheme that allows for an…
A new code, named MAP, is written in Fortran language for magnetohydrodynamics (MHD) calculation with the adaptive mesh refinement (AMR) and Message Passing Interface (MPI) parallelization. There are several optional numerical schemes for…
We investigate the ideal and incompressible magnetohydrodynamic (MHD) equations in three space dimensions for the development of potentially singular structures. The methodology consists in implementing the four-fold symmetries of the…
We develop a new numerical scheme for ideal magnetohydrodynamic (MHD) simulations, which is robust against one- and multi-dimensional shocks, and is accurate for low Mach number flows and discontinuities. The scheme belongs to a family of…
We study a general convergence theory for the analysis of numerical solutions to the magnetohydrodynamic system describing the time evolution of compressible, viscous, electrically conducting fluids in space dimension d (= 2; 3). First, we…
In this paper we generalize the method of Lagrangian descriptors to two dimensional, area preserving, autonomous and nonautonomous discrete time dynamical systems. We consider four generic model problems--a hyperbolic saddle point for a…
In this paper we propose and analyze a mixed DG method and an HDG method for the stationary Magnetohydrodynamics (MHD) equations with two types of boundary (or constraint) conditions. The mixed DG method is based a recent work proposed by…
We introduce a time-dimensional reduction method for the inverse source problem in linear elasticity, where the goal is to reconstruct the initial displacement and velocity fields from partial boundary measurements of elastic wave…