Finite element quasi-interpolation and best approximation
Abstract
This paper introduces a quasi-interpolation operator for scalar- and vector-valued finite element spaces constructed on affine, shape-regular meshes with some continuity across mesh interfaces. This operator gives optimal estimates of the best approximation error in any Lp-norm assuming regularity in the fractional Sobolev spaces Wr,p, where p ∈ [ 1,∞ ] and the smoothness index r can be arbitrarily close to zero. The operator is stable in L1, leaves the corresponding finite element space point-wise invariant, and can be modified to handle homogeneous boundary conditions. The theory is illustrated on H1-, H(curl)- and H(div)-conforming spaces.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jul 01, 2017
- Source ID
- 10.1051/m2an/2016066
Entities
People
- Alexandre Ern
- Jean-luc Guermond
Organizations
- Air Force Office of Scientific Research
- Army Research Office
- National Science Foundation