Abstract
We study a new mixed finite element of lowest order for general quadrilateral grids which gives optimal order error in the H(div)-norm. This new element is designed so that the H(div)-projection Π h satisfies ∇ · Π h = P h div. A rigorous optimal order error estimate is carried out by proving a modified version of the Bramble–Hilbert lemma for vector variables. We show that a local H(div)-projection reproducing certain polynomials suffices to yield an optimal L 2-error estimate for the velocity and hence our approach also provides an improved error estimate for original Raviart–Thomas element of lowest order. Numerical experiments are presented to verify our theory.
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