Browsing Matematisk institutt by Author "Falk, Richard S."

Now showing items 1-5 of 5

  • The Bubble Transform: A New Tool for Analysis of Finite Element Methods 
    Falk, Richard S.; Winther, Ragnar (Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2015)
    The purpose of this paper is to discuss the construction of a linear operator, referred to as the bubble transform, which maps scalar functions defined on Ω⊂Rn into a collection of functions with local support. In fact, ...
  • CONSTRUCTION OF POLYNOMIAL PRESERVING COCHAIN EXTENSIONS BY BLENDING 
    Falk, Richard S.; Winther, Ragnar (Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2023)
    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 blending functions. The purpose of this paper is ...
  • Double complexes and local cochain projections 
    Falk, Richard S.; Winther, Ragnar (Journal article / Tidsskriftartikkel / PublishedVersion; Peer reviewed, 2015)
    The construction of projection operators, which commute with the exterior derivative and at the same time are bounded in the proper Sobolev spaces, represents a key tool in the recent stability analysis of finite element ...
  • Local bounded cochain projections 
    Falk, Richard S.; Winther, Ragnar (Journal article / Tidsskriftartikkel / PublishedVersion; Peer reviewed, 2014)
    First published in Mathematics of Computation Mathematics of Computation. 2014, 83 (290), published by the American Mathematical Society.
  • The Bubble Transform and the de Rham Complex 
    Falk, Richard S.; Winther, Ragnar (Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2022)
    The purpose of this paper is to discuss a generalization of the bubble transform to differential forms. The bubble transform was discussed in Falk and Winther (Found Comput Math 16(1):297–328, 2016) for scalar valued ...