Abstract
This paper discusses convergence and complexity of arbitrary, but fixed, order adaptive mixed element methods for the Poisson equation in two and three dimensions. The two main ingredients in the analysis, namely the quasi-orthogonality and the discrete reliability, are achieved by use of a discrete Helmholtz decomposition and a discrete inf-sup condition. The adaptive algorithms are shown to be contractive for the sum of the error of flux in L 2-norm and the scaled error estimator after each step of mesh refinement and to be quasi-optimal with respect to the number of elements of underlying partitions. The methods do not require a separate treatment for the data oscillation.
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Huang, J., Xu, Y. Convergence and complexity of arbitrary order adaptive mixed element methods for the Poisson equation. Sci. China Math. 55, 1083–1098 (2012). https://doi.org/10.1007/s11425-012-4384-0
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DOI: https://doi.org/10.1007/s11425-012-4384-0
Keywords
- mixed element method
- a posteriori error estimate
- adaptive finite element method
- convergence
- computational complexity