An augmented Lagrangian preconditioner for the magnetohydrodynamics equations at high Reynolds and coupling numbers
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 …
numerically, due to their highly nonlinear structure and the strong coupling between the …
Immersed virtual element methods for electromagnetic interface problems in three dimensions
Finite element methods for electromagnetic problems modeled by Maxwell-type equations
are highly sensitive to the conformity of approximation spaces, and non-conforming methods …
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 …
Specifically, stable equivalent mixed formulations for the model problems are presented …
Transformed primal–dual methods for nonlinear saddle point systems
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 …
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 …
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 …
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
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 …
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
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 …
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 …
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
A block-diagonal preconditioner with the minimal residual method and an approximate block-
factorization preconditioner with the generalized minimal residual method are developed for …
factorization preconditioner with the generalized minimal residual method are developed for …