A stable and H1-conforming divergence-free finite element pair for the Stokes problem using isoparametric mappings.

This paper expands the isoparametric framework to construct a stable, H 1 -conforming, and divergence-free method for the Stokes problem in two dimensions based on the Scott-Vogelius pair on Clough-Tocher splits. The pressure space is defined through composition, whereas the velocity space is constructed via a new divergence-preserving mapping that imposes full continuity across shared edges in the isoparametric mesh. Our construction is motivated by operators and spaces found in isoparametric C 1 finite element methods. We prove the method is stable, pressure-robust, and has optimal order convergence. Numerical experiments are provided which confirm the theoretical results. [ABSTRACT FROM AUTHOR]