caa a22 4500 445862092 CHVBK 20180317145446.0 cr unu---uuuuu 170323e20110901xx s 000 0 eng 10.1007/s10092-010-0035-4 doi (NATIONALLICENCE)springer-10.1007/s10092-010-0035-4 Zhang Shangyou Department of Mathematical Sciences, University of Delaware, 19716, Newark, DE, USA aut Quadratic divergence-free finite elements onPowell-Sabin tetrahedral grids [Elektronische Daten] [Shangyou Zhang] Given a tetrahedral grid in 3D, a Powell-Sabin grid can be constructed by refining each original tetrahedron into 12 subtetrahedra. A new divergence-free finite element on 3D Powell-Sabin grids is constructed for Stokes equations, where the velocity is approximated by continuous piecewise quadratic polynomials while the pressure is approximated by discontinuous piecewise linear polynomials on the same grid. To be precise, the finite element space for the pressure is exactly the divergence of the corresponding space for the velocity. Therefore, the resulting finite element solution for the velocity is pointwise divergence-free, including the inter-element boundary. By establishing the inf-sup condition, the finite element is stable and of the optimal order. Numerical tests are provided. Springer-Verlag, 2010 Mixed finite element nationallicence Stokes equations nationallicence Divergence-free element nationallicence Tetrahedral grid nationallicence Powell-Sabin grid nationallicence Calcolo Springer Milan 48/3(2011-09-01), 211-244 0008-0624 48:3<211 2011 48 10092 https://doi.org/10.1007/s10092-010-0035-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10092-010-0035-4 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Zhang Shangyou Department of Mathematical Sciences, University of Delaware, 19716, Newark, DE, USA aut NATIONALLICENCE 773 0- Calcolo Springer Milan 48/3(2011-09-01), 211-244 0008-0624 48:3<211 2011 48 10092 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer