On commuting $p$-version projection-based interpolation on tetrahedra

Abstract

On the reference tetrahedron $\hat{K}$, we define three projection-based interpolation operators on $H^2(\hat{K})$, ${\mathbf{H}}^1(\hat{K},\mathrm{curl})$, and ${\mathbf{H}}^1(\hat{K},\mathrm{div})$. These operators are projections onto space of polynomials, they have the commuting diagram property and feature the optimal convergence rate as the polynomial degree increases in $H^{1-s}(\hat{K})$, ${\mathbf{H}}^{-s}(\hat{K},\mathrm{curl})$, ${\mathbf{H}}^{-s}(\hat{K},\mathrm{div})$ for $0\le s\le 1$.

References in corpus (3)

• Discrete compactness for the p-version of discrete differential forms
• Optimal error estimation for H(curl)-conforming p-interpolation in two dimensions
• Discrete Compactness for p-Version of Tetrahedral Edge Elements

Cited by in corpus (8)

• Wavenumber-explicit $hp$-FEM analysis for Maxwell's equations with transparent boundary conditions
• Error estimates for the Scaled Boundary Finite Element Method
• Analysis of the $hp$-version of a first order system least squares method for the Helmholtz equation
• Optimal convergence rates in $L^2$ for a first order system least squares finite element method. Part I: homogeneous boundary conditions
• Equivalence of local-and global-best approximations, a simple stable local commuting projector, and optimal $hp$ approximation estimates in $H(\mathrm{div})$
• Adaptive hybrid high-order method for guaranteed lower eigenvalue bounds
• Exponential meshes and $\mathcal{H}$-matrices
• Local $L^2$-bounded commuting projections in FEEC