相关论文: Degenerate anisotropic elliptic problems and magne…

The aim of this work is to show an abstract framework to analyze the numerical approximation for a family of linear degenerate parabolic mixed equations by using a finite element method in space and a Backward-Euler scheme in time. We…

We prove estimates for weak solutions to a class of Dirichlet problems associated to anisotropic elliptic equations with a zero order term.

The isentropic vortex problem is frequently solved to test the accuracy of numerical methods and verify corresponding code. Unfortunately, its existing solution was derived in the relativistic magnetohydrodynamics by numerically solving an…

We study a nonlinear system made up of an elliptic equation of blended singular/degenerate type and Poisson's equation with a lowly integrable source. We prove the existence of a weak solution in any space dimension and, chiefly, derive an…

Finite difference based micromagnetic simulations are a powerful tool for the computational investigation of magnetic structures. In this paper, we demonstrate how the discretization of continuous micromagnetic equations introduces a…

We investigate nonlinear elliptic Dirichlet problems whose growth is driven by a general anisotropic $N$-function, which is not necessarily of power type and need not satisfy the $\Delta_2$ nor the $\nabla _2$-condition. Fully anisotropic,…

In this paper, a new asymptotic preserving (AP) scheme is proposed for the anisotropic elliptic equations. Different from previous AP schemes, the actual one is based on first-order system least-squares for second-order partial differential…

We present a general approach to the derivation of the effective anisotropy field which determines the dynamical behaviour of magnetic spins according to the Landau-Lifshitz-Gilbert equation. The approach is based on the gradient in…

A simple and efficient interface-fitted mesh generation algorithm is developed in this paper. This algorithm can produce a local anisotropic fitting mixed mesh which consists of both triangles and quadrilaterals near the interface. A new…

The goal of this paper is to study some possibly degenerate elliptic equation in a bounded domain with a nonlinear boundary condition involving measure data. We investigate two types of problems: the first one deals with the laplacian in a…

We describe a new model for the study of weakly-collisional, magnetized plasmas derived from exploiting the separation of the dynamics parallel and perpendicular to the magnetic field. This unique system of equations retains the particle…

In this paper we propose a finite element method for solving elliptic equations with the observational Dirichlet boundary data which may subject to random noises. The method is based on the weak formulation of Lagrangian multiplier. We show…

We introduce a new iterative method for computing solutions of elliptic equations with random rapidly oscillating coefficients. Similarly to a multigrid method, each step of the iteration involves different computations meant to address…

A numerical scheme is developed for systems of conservation laws on manifolds which arise in high speed aerodynamics and magneto-aerodynamics. The systems are presented in an arbitrary coordinate system on the manifold and involve source…

Micromagnetics depends on high-fidelity numerical methods for magnetization dynamics. This work proposes a third-order temporal accuracy scheme for the Landau-Lifshitz-Gilbert equation, addressing accuracy-efficiency trade-offs in existing…

Distortions in the electron distribution function driven by intense temperature gradients critically influence the generation and evolution of heat flux and magnetic fields in plasmas under the condition of inertial confinement fusion.…

This work belongs to the framework of inverse problems with linear model. The resolution of this type of problem consists in minimizing (possibly under constraints) a function of discrepancy between the measurements and a physical model of…

Anisotropy of a space naturally leads to direction dependent electromagnetic tensors and electromagnetic potentials. Starting from this idea and using variational approaches and exterior derivative formalism, we extend some of the classical…

Multiple solutions are common in various non-convex problems arising from industrial and scientific computing. Nonetheless, understanding the nontrivial solutions' qualitative properties seems limited, partially due to the lack of efficient…

Astrophysical fluids under the influence of magnetic fields are often subjected to single-fluid or two-fluid approximations. In the case of weakly ionized plasmas however, this can be inappropriate due to distinct responses from the…