Bonito, Andrea; Burman, Erik A face penalty method for the three-field Stokes equation arising from Oldroyd-B viscoelastic flows. (English) Zbl 1119.76039 Bermúdez de Castro, Alfredo (ed.) et al., Numerical mathematics and advanced applications. Proceedings of ENUMATH 2005, the 6th European conference on numerical mathematics and advanced applications, Santiago de Compostela, Spain, July 18–22, 2005. Berlin: Springer (ISBN 3-540-34287-7/hbk). 487-494 (2006). Summary: We apply the continuous interior penalty method to the three-field Stokes problem. We prove an inf-sup condition for the proposed method leading to optimal a priori error estimates for smooth exact solutions. Moreover, we propose an iterative algorithm for the separate solution of velocities and pressures on the one hand and the extra-stress on the other. The stability of the iterative algorithm is established.For the entire collection see [Zbl 1103.65002]. Cited in 3 Documents MSC: 76M10 Finite element methods applied to problems in fluid mechanics 76A10 Viscoelastic fluids Keywords:iterative algorithm; inf-sup condition; a priori error estimates PDFBibTeX XMLCite \textit{A. Bonito} and \textit{E. Burman}, in: Numerical mathematics and advanced applications. Proceedings of ENUMATH 2005, the 6th European conference on numerical mathematics and advanced applications, Santiago de Compostela, Spain, July 18--22, 2005. Berlin: Springer. 487--494 (2006; Zbl 1119.76039)