FIRST-ORDER SYSTEM LEAST SQUARES ON CURVED BOUNDARIES: LOWEST-ORDER RAVIART-THOMAS ELEMENTS

The effect of interpolated edges of curved boundaries on Raviart-Thomas finite element approximations is studied in this paper in the context of first-order system least squares methods. In particular, it is shown that an optimal order of convergence is achieved for lowest-order elements on a polygonal domain. This is illustrated numerically for an elliptic boundary value problem involving circular curves. The computational results also show that a polygonal approximation is not sufficient to achieve convergence of optimal order in the higher-order case.