An augmented Lagrangian preconditioner for the magnetohydrodynamics equations at high Reynolds and coupling numbers

F Laakmann, PE Farrell, L Mitchell - SIAM Journal on Scientific Computing, 2022 - SIAM
The magnetohydrodynamics (MHD) equations are generally known to be difficult to solve
numerically, due to their highly nonlinear structure and the strong coupling between the …

Immersed virtual element methods for electromagnetic interface problems in three dimensions

S Cao, L Chen, R Guo - … Models and Methods in Applied Sciences, 2023 - World Scientific
Finite element methods for electromagnetic problems modeled by Maxwell-type equations
are highly sensitive to the conformity of approximation spaces, and non-conforming methods …

Mixed schemes for quad-curl equations

S Zhang - ESAIM: Mathematical Modelling and Numerical …, 2018 - numdam.org
In this paper, mixed schemes are presented for two variants of quad-curl equations.
Specifically, stable equivalent mixed formulations for the model problems are presented …

Transformed primal–dual methods for nonlinear saddle point systems

L Chen, J Wei - Journal of Numerical Mathematics, 2023 - degruyter.com
A transformed primal–dual (TPD) flow is developed for a class of nonlinear smooth saddle
point systemThe flow for the dual variable contains a Schur complement which is strongly …

Energy-preserving mixed finite element methods for the elastic wave equation

S Li, Y Wu - Applied Mathematics and Computation, 2022 - Elsevier
In this paper, energy-preserving mixed finite element methods corresponding to finite
element exterior calculus are constructed for the first-order formulation of the elastic wave …

Nonconforming finite element Stokes complexes in three dimensions

X Huang - Science China Mathematics, 2023 - Springer
Two nonconforming finite element Stokes complexes starting from the conforming Lagrange
element and ending with the nonconforming P 1-P 0 element for the Stokes equation in …

Decoupling of mixed methods based on generalized Helmholtz decompositions

L Chen, X Huang - SIAM Journal on Numerical Analysis, 2018 - SIAM
A framework to systematically decouple high order elliptic equations into a combination of
Poisson-type and Stokes-type equations is developed. The key is to systematically construct …

Optimal Analysis of Non-Uniform Galerkin-Mixed Finite Element Approximations to the Ginzburg–Landau Equations in Superconductivity

H Gao, W Sun - SIAM Journal on Numerical Analysis, 2023 - SIAM
This paper is concerned with new error analysis of a lowest-order backward Euler Galerkin-
mixed finite element method for the time-dependent Ginzburg–Landau equations. The …

Energy-stable mixed finite element methods for a ferrofluid flow model

Y Wu, X Xie - Communications in Nonlinear Science and Numerical …, 2023 - Elsevier
In this paper, we develop a class of mixed finite element methods for the ferrofluid flow
model proposed by Shliomis (1972). We show that the energy stability of the weak solutions …

Fast auxiliary space preconditioners for linear elasticity in mixed form

L Chen, J Hu, X Huang - Mathematics of Computation, 2018 - ams.org
A block-diagonal preconditioner with the minimal residual method and an approximate block-
factorization preconditioner with the generalized minimal residual method are developed for …