We consider a singular perturbation problem which describes 2D Darcy-Stokes flow. An H(div)-conforming rectangular element, DS-R14, is proposed and analyzed first. This element has 14 degrees of freedom for velocity and is proved to be uniformly convergent with respect to perturbation constant. We then simplify this element to get another H(div)-conforming rectangular element, DS-R12, which has 12 degrees of freedom for velocity. The uniform convergence is also obtained for this element. Finally, we construct a de Rham complex corresponding to DS-R12 element.
- Darcy-Stokes problem
- H(div)-conforming rectangular elements
- uniform convergence
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