PETSCSPACEPTRIMMED#

Notes#

Trimmed polynomial spaces correspond to several common conformal approximation spaces in the de Rham complex#

In $H^1$ ($\sim k=0$), trimmed polynomial spaces are identical to the standard polynomial spaces, $\mathcal{P}_r^- \sim P_r$.

In $H(\text{curl})$, ($\sim k=1$), trimmed polynomial spaces are equivalent to $H(\text{curl})$-Nedelec spaces of the first kind and can be written as $\begin{cases} [P_{r-1}(\mathbb{R}^2)]^2 \oplus \mathrm{rot}(\bf{x}) H_{r-1}(\mathbb{R}^2), & n = 2, \\ [P_{r-1}(\mathbb{R}^3)]^3 \oplus \bf{x} \times [H_{r-1}(\mathbb{R}^3)]^3, & n = 3. \end{cases}$

In $H(\text{div})$ ($\sim k=n-1$), trimmed polynomial spaces are equivalent to Raviart-Thomas spaces ($n=2$) and $H(\text{div})$-Nedelec spaces of the first kind ($n=3$), and can be written as $[P_{r-1}(\mathbb{R}^n)]^n \oplus \bf{x} H_{r-1}(\mathbb{R}^n).$

In $L_2$, ($\sim k=n$), trimmed polynomial spaces are identical to the standard polynomial spaces of one degree less, $\mathcal{P}_r^- \sim P_{r-1}$.

See Also#

PetscSpace, PetscSpaceType, PetscSpaceCreate(), PetscSpaceSetType(), PetscDTPTrimmedEvalJet()

Level#

intermediate

Location#

src/dm/dt/space/impls/ptrimmed/spaceptrimmed.c

Index of all SPACE routines
Table of Contents for all manual pages
Index of all manual pages