ABSTRACT
The Galerkin finite element discretization of the saddle-point problem (2.5) - (2.7) uses subspaces C H and Qh C Q of piecewise polynomial functions defined on regular decompositions Th = UTen^i^} of the domain Q into cells T (triangles or quadrilaterals); see Brenner and Scott [5]. Here, we think of bilinear shape functions. In order to avoid unnecessary complications due to curved boundaries, we suppose the domain Q to be polygonal. We use the notation hr := diam(T) and hr := diam(T) for the width of a cell T E T/* or a cell edge T C dQ . In order to ease local mesh refinement and coarsening, hanging nodes are allowed but at most one per edge; see Figure 3.1. The
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Figure 3.1: Quadrilateral mesh with “hanging nodes” .
