@Article{IJNAM-21-2,
author = {M., Jeffrey, Connors and Michael, Gaiewski},
title = {An $H^1$-Conforming Solenoidal Basis for Velocity Computation on Powell-Sabin Splits for the Stokes Problem},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2024},
volume = {21},
number = {2},
pages = {181--200},
abstract = {<p style="text-align: justify;">A solenoidal basis is constructed to compute velocities using a certain finite element
method for the Stokes problem. The method is conforming, with piecewise linear velocity and
piecewise constant pressure on the Powell-Sabin split of a triangulation. Inhomogeneous Dirichlet
conditions are supported by constructing an interpolating operator into the solenoidal velocity
space. The solenoidal basis reduces the problem size and eliminates the pressure variable from the
linear system for the velocity. A basis of the pressure space is also constructed that can be used to
compute the pressure after the velocity, if it is desired to compute the pressure. All basis functions
have local support and lead to sparse linear systems. The basis construction is confirmed through
rigorous analysis. Velocity and pressure system matrices are both symmetric, positive definite,
which can be exploited to solve their corresponding linear systems. Significant efficiency gains
over the usual saddle-point formulation are demonstrated computationally.</p>},
issn = {2617-8710},
doi = {https://doi.org/10.4208/ijnam2024-1007},
url = {https://global-sci.com/article/91054/an-h1-conforming-solenoidal-basis-for-velocity-computation-on-powell-sabin-splits-for-the-stokes-problem}
}