Summary
We consider the mixed finite element method for locally refined triangulations. A local projection operator\(\hat \Pi _h \) is defined to satisfy the commutation property that is required in the general theory of mixed methods. Our results can be applied to every known space of arbitrary order over rectangles or triangles. Optimal-order error estimates and superconvergence for the flux along the Gauss lines are established.
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Ewing, R.E., Wang, J. Analysis of mixed finite element methods on locally refined grids. Numer. Math. 63, 183–194 (1992). https://doi.org/10.1007/BF01385855
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DOI: https://doi.org/10.1007/BF01385855