Summary.
We consider the mixed formulation for the elasticity problem and the limiting Stokes problem in \({\Bbb R}^d\),\(d=2,3\) . We derive a set of sufficient conditions under which families of mixed finite element spaces are simultaneously stable with respect to the mesh size\(h\) and, subject to a maximum loss of\(O (k^{\frac{d-1}{2}})\) , with respect to the polynomial degree \(k\). We obtain asymptotic rates of convergence that are optimal up to\(O (k^\epsilon)\) in the displacement/velocity and up to\(O (k^{\frac{d-1}{2}+\epsilon})\) in the "pressure", with\(\epsilon >0\) arbitrary (both rates being optimal with respect to\(h\) ). Several choices of elements are discussed with reference to properties desirable in the context of the \(hp\)-version.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Author information
Authors and Affiliations
Additional information
Received March 4, 1994 / Revised version received February 12, 1995
Rights and permissions
About this article
Cite this article
Stenberg, R., Suri, M. Mixed \(hp\) finite element methods for problems in elasticity and Stokes flow . Numer. Math. 72, 367–389 (1996). https://doi.org/10.1007/s002110050174
Issue Date:
DOI: https://doi.org/10.1007/s002110050174