A Local Projection Stabilization FEM for the Linearized Stationary MHD Problem
نویسندگان
چکیده
We present a local projection stabilization (LPS) type finite element (FE) method for the linearized stationary magnetohydrodynamics (MHD) problem which is essentially based on the ideas of the residual-based stabilization given in [1], [2], [3]. In contrast to the residual-based stabilization, we investigate a symmetric LPS comparable to the term-by-term stabilization in [3].
منابع مشابه
Local Boundary Feedback Stabilization of the Navier-Stokes Equations
We study the exponential stabilization of the linearized Navier-Stokes equations around an unstable stationary solution, by means of a feedback boundary control, in dimension 2 or 3. The feedback law is determined by solving a Linear-Quadratic control problem. We do not assume that the normal component of the control is equal to zero. In that case the state equation, satisfied by the velocity f...
متن کاملStabilization of linearized 2D magnetohydrodynamic channel flow by backstepping boundary control
We present a boundary control law that stabilizes the Hartman profile for low magnetic Reynolds numbers in an infinite magnetohydrodynamic (MHD) channel flow. The proposed control law achieves stability in the L2 norm of the linearized MHD equations, guaranteeing local stability for the fully nonlinear system. © 2008 Elsevier B.V. All rights reserved.
متن کاملFeedback Boundary Stabilization of the Two-Dimensional Navier--Stokes Equations
We study the exponential stabilization of the linearized Navier-Stokes equations around an unstable stationary solution, by means of a feedback boundary control, in dimension 2 or 3. The feedback law is determined by solving a Linear-Quadratic control problem. We do not assume that the normal component of the control is equal to zero. In that case the state equation, satisfied by the velocity f...
متن کامل10th International Workshop on Variational Multiscale and Stabilized Finite Elements (VMS2015)
for 10th International Workshop on Variational Multiscale and Stabilized Finite Elements (VMS2015) Some open problems of inf-sup stable FEM for incompressible flow problems G. Lube∗ Georg-August University Göttingen, Institute for Numerical and Applied Mathematics [email protected] In this talk, I will address some open problems occuring in the numerical approximation of incompressibl...
متن کاملFeedback Stabilization of Two Dimensional Magnetohydrodynamic Equations*
We prove the local exponential stabilizability for the MHD system in space dimension 2, with internally distributed feedback controllers. These controllers take values in a finite dimensional space which is the unstable manifold of the elliptic part of the linearized operator. They are represented through two scalar functions supported in a subdomain. Mathematics Subject Classification 2000: 93...
متن کامل