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1.
A posteriori error estimation for the Stokes–Darcy coupled problem on anisotropic discretization
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Koffi Wilfrid Houedanou Bernardin Ahounou 《Mathematical Methods in the Applied Sciences》2017,40(10):3741-3774
This paper presents an a posteriori error analysis for the stationary Stokes–Darcy coupled problem approximated by finite element methods on anisotropic meshes in or 3. Korn's inequality for piecewise linear vector fields on anisotropic meshes is established and is applied to non‐conforming finite element method. Then the existence and uniqueness of the approximation solution are deduced for non‐conforming case. With the obtained finite element solutions, the error estimators are constructed and based on the residual of model equations plus the stabilization terms. The lower error bound is proved by means of bubble functions and the corresponding anisotropic inverse inequalities. In order to prove the upper error bound, it is vital that an anisotropic mesh corresponds to the anisotropic function under consideration. To measure this correspondence, a so‐called matching function is defined, and its discussion shows it to be useful tool. With its help, the upper error bound is shown by means of the corresponding anisotropic interpolation estimates and a special Helmholtz decomposition in both media. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
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Recent algebraic parametric estimation techniques (see Fliess and Sira-Ramírez, ESAIM Control Optim Calc Variat 9:151–168,
2003, 2008) led to point-wise derivative estimates by using only the iterated integral of a noisy observation signal (see Mboup et al.
2007, Numer Algorithms 50(4):439–467, 2009). In this paper, we extend such differentiation methods by providing a larger choice of parameters in these integrals: they
can be reals. For this, the extension is done via a truncated Jacobi orthogonal series expansion. Then, the noise error contribution
of these derivative estimations is investigated: after proving the existence of such integral with a stochastic process noise,
their statistical properties (mean value, variance and covariance) are analyzed. In particular, the following important results
are obtained:
(a) |
the bias error term, due to the truncation, can be reduced by tuning the parameters, 相似文献
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Philip A. Ernst Wilfrid S. Kendall Gareth O. Roberts Jeffrey S. Rosenthal 《Stochastic Processes and their Applications》2019,129(2):355-380
Classical coupling constructions arrange for copies of the same Markov process started at two different initial states to become equal as soon as possible. In this paper, we consider an alternative coupling framework in which one seeks to arrange for two different Markov (or other stochastic) processes to remain equal for as long as possible, when started in the same state. We refer to this “un-coupling” or “maximal agreement” construction as MEXIT, standing for “maximal exit”. After highlighting the importance of un-coupling arguments in a few key statistical and probabilistic settings, we develop an explicit MEXIT construction for stochastic processes in discrete time with countable state-space. This construction is generalized to random processes on general state-space running in continuous time, and then exemplified by discussion of MEXIT for Brownian motions with two different constant drifts. 相似文献
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Wilfrid Oberhummer 《Monatshefte für Chemie / Chemical Monthly》1933,63(1-2):285-300
Ohne Zusammenfassung 相似文献
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Wilfrid Gangbo 《偏微分方程通讯》2013,38(9):1041-1073
We introduce a new variational time discretization for the system of isentropic Euler equations. In each timestep the internal energy is reduced as much as possible, subject to a constraint imposed by a new cost functional that measures the deviation of particles from their characteristic paths. 相似文献
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