For a nonconforming finite element approximation of an elliptic model problem, we propose a posteriori error estimates in the energy norm which use as an additive term the “post-processing error” between the original nonconforming finite element solution and an easy computable conforming approximation of that solution. Thus, for the error analysis, the existing theory from the conforming case can be used together with some simple additional arguments. As an essential point, the property is exploited...
We consider a family of quadrilateral or hexahedral
mixed -finite elements for an incompressible
flow problem with
-elements for the velocity and
discontinuous -elements for the pressure where the order
can vary from element to element
between and an arbitrary bound.
For multilevel adaptive grids
with hanging nodes and a sufficiently small mesh size,
we prove the inf-sup condition uniformly with respect to the mesh
size and the polynomial degree.
For a nonconforming finite element approximation of an elliptic model
problem, we propose error estimates in the energy norm
which use as an additive term the “post-processing error” between
the original nonconforming finite element solution and an easy
computable conforming approximation of that solution.
Thus, for the error analysis, the existing theory from the conforming
case can be used together with some simple additional arguments.
As an essential point, the property is exploited that...
This paper presents a postprocessing technique for estimating the local regularity of numerical solutions in high-resolution finite element schemes. A derivative of degree p ≥ 0 is considered to be smooth if a discontinuous linear reconstruction does not create new maxima or minima. The intended use of this criterion is the identification of smooth cells in the context of p-adaptation or selective flux limiting. As a model problem, we consider a 2D convection equation discretized with bilinear finite...
We consider higher order mixed finite element methods for the incompressible
Stokes or Navier-Stokes equations with
-elements for the velocity and
discontinuous -elements for the pressure where the order
can vary from element to element
between and a fixed bound .
We prove the inf-sup condition uniformly with respect to the meshwidth
on general quadrilateral and hexahedral meshes with hanging nodes.
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