A quadratic finite element wavelet Riesz basis
This work provides a new wavelet basis for numerical methods on polygonal domains, but the results are incremental as they extend existing linear wavelet constructions to quadratic elements.
The authors construct continuous piecewise quadratic finite element wavelets on general polygons in R^2 that are stable in H^s for |s|<3/2 with two vanishing moments, and provide numerically computed condition numbers for the unit square.
In this paper, continuous piecewise quadratic finite element wavelets are constructed on general polygons in $\mathbb{R}^2$. The wavelets are stable in $H^s$ for $|s|<\frac{3}{2}$ and have two vanishing moments. Each wavelet is a linear combination of 11 or 13 nodal basis functions. Numerically computed condition numbers for $s \in \{-1,0,1\}$ are provided for the unit square.