TR-2019-18
C1 Piecewise Polynomials Satisfying Boundary Conditions
L. Ridgway Scott. 11 November, 2019.
Communicated by L. Ridgway Scott.
Abstract
We construct a nodal basis for C1 piecewise polynomials of degree 4 on a triangulated polygonal domain in the plane. Our results confirm a conjecture of Strang.We determine the support of the corresponding basis functions in certain cases.In such cases, we are able to compute the dimension of the space of C1 piecewise polynomials of degree 4 that vanish to second order on the boundary. This provides an alternative approach to determining the number of spurious modes for piecewise cubics in the Stokes problem.
We also examine C1 piecewise polynomials of degree less than 4, on special meshes, that vanish to to second order on the boundary.
Original Document
The original document is available in PDF (uploaded 11 November, 2019 by L. Ridgway Scott).