Abstract:
We construct an operator that preserves the discrete divergence and has the same quasi-local approximation properties as a regularizing interpolant; this is very useful when discretizing nonlinear incompressible fluid models. For low-degree finite elements, such operators have an explicit expression, from which local approximation properties can be easily derived. But for higher-degree finite elements, an explicit expression is generally not available and this construction is achieved by proving a global discrete inf–sup condition while using only local arguments. We write this construction in a general case, for conforming and non-conforming elements, and then give some applications.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: June 2002 / Accepted: September 2002
Rights and permissions
About this article
Cite this article
Girault, V., Scott, L. A quasi-local interpolation operator¶preserving the discrete divergence. CALCOLO 40, 1–19 (2003). https://doi.org/10.1007/s100920300000
Issue Date:
DOI: https://doi.org/10.1007/s100920300000