Multigrid Methods for a Stabilized Reissner–Mindlin Plate Formulation

Multigrid Methods for a Stabilized Reissner-Mindlin Plate Formulation

We consider a stabilized finite element formulation for the Reissner-Mindlin plate bending model. The method uses standard bases functions for the deflection and the rotation vector. We apply a standard multigrid algorithm to obtain a preconditioner. We prove that the condition number of the preconditioned system is uniformly bounded with respect to the multigrid level and the thickness paramet...

Multigrid methods for stabilized nonconforming finite elements for incompressible flow involving the deformation tensor formulation

Edge-oriented stabilization methods in the framework of discontinuous Galerkin approaches have been recently proposed by Brenner [3] and particularly by Hansbo and Larson [5] for nonconforming finite element discretizations to satisfy a discrete Korn’s inequality. We develop and analyse corresponding multigrid components in combination with local Pressure-Schur-Complement methods and give numer...

Generic programming and algebraic multigrid for stabilized finite element methods

A stabilized difference scheme for deformable porous media and its numerical resolution by multigrid methods

This paper deals with the 2D system of incompressible poroelasticity equations inwhich an artificial stabilization term has been added to the discretization on collocated grids. Two issues are discussed: It is proved and shown that the additional term indeedbrings stability and does not spoil the second order accurate convergence. Secondly, various smoothers are examined in order to find an opt...

A stabilized multigrid solver for hyperelastic image registration

Correspondence Lars Ruthotto, Department of Mathematics and Computer Science, Emory University, 400 Dowman Dr, Atlanta, GA 30322, USA. Email: [email protected] Summary Image registration is a central problem in a variety of areas involving imaging techniques and is known to be challenging and ill-posed. Regularization functionals based on hyperelasticity provide a powerful mechanism for limit...