Section: New Results
Finite element quasi-interpolation and best-approximation
Participant : Alexandre Ern.
Publication: [21]
In [21], we introduce 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 -norm assuming regularity in the fractional Sobolev spaces , where and the smoothness index can be arbitrarily close to zero. The operator is stable in , leaves the corresponding finite element space point-wise invariant, and can be modified to handle homogeneous boundary conditions. The theory is illustrated on -, -, and -conforming spaces.