7 papers
Local space-preserving decompositions for the bubble transform
Richard S. Falk, Ragnar Winther
The bubble transform is a procedure to decompose differential forms, which are piecewise smooth with respect to a given triangulation of the domain, into a sum of local bubbles. In…
A uniform preconditioner for a Newton algorithm for total-variation minimization and minimum-surface problems
Xue-Cheng Tai, Ragnar Winther, Xiaodi Zhang +1
Solution methods for the nonlinear partial differential equation of the Rudin-Osher-Fatemi (ROF) and minimum-surface models are fundamental for many modern applications. Many effic…
Construction of polynomial preserving cochain extensions by blending
Richard S. Falk, Ragnar Winther
A classical technique to construct polynomial preserving extensions of scalar functions defined on the boundary of an simplex to the interior is to use so-called rational blend…
The Bubble Transform and the de Rham Complex
Richard S. Falk, Ragnar Winther
The purpose of this paper is to discuss a generalization of the bubble transform to differential forms. The bubble transform was discussed in a previous paper by the authors for sc…
Well-conditioned frames for high order finite element methods
Kaibo Hu, Ragnar Winther
The purpose of this paper is to discuss representations of high order finite element spaces on simplicial meshes in any dimension. When computing with high order piecewise po…
Weakly imposed symmetry and robust preconditioners for Biot's consolidation model
Trygve Baerland, Jeonghun J. Lee, Kent-Andre Mardal +1
We discuss the construction of robust preconditioners for finite element approximations of Biot's consolidation model in poroelasticity. More precisely, we study finite element met…