Abstract
In this paper we will concentrate on the numerical solution of the Cauchy–Riemann equations. First we show that these equations bring together the finite element discretizations for the Laplace equation by standard finite elements on the one hand, and by mixed finite element methods on the other. As a consequence, methods for a posteriori error estimation for both finite element methods can derive their validity from each other. Moreover, we show that given a finite element approximation of one of the vectorfields, the missing can be accurately computed in optimal complexity.
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Brandts, J. The Cauchy–Riemann Equations: Discretization by Finite Elements, Fast Solution of the Second Variable, and a Posteriori Error Estimation. Advances in Computational Mathematics 15, 61–77 (2001). https://doi.org/10.1023/A:1014217225870
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DOI: https://doi.org/10.1023/A:1014217225870