Quasi-optimal a priori estimates for fluxes in mixed finite element methods and an application to the Stokes-Darcy coupling

摘要

We show improved a priori convergence results in the L~2 norm on interfaces for the approximation of the normal component of the flux in mixed finite element methods. Compared with standard estimates for this problem class, additional factors of √h| log h| for the lowest-order case and of √h in the higherorder case in the a priori bound for the flux variable are obtained. An important role in the analysis play new error estimates in strips of width O(h) and the use of anisotropic and weighted norms. Numerical examples including an application to the Stokes-Darcy coupling illustrate our theoretical results.