116,039 research outputs found
Convergence and optimality of the adaptive nonconforming linear element method for the Stokes problem
In this paper, we analyze the convergence and optimality of a standard
adaptive nonconforming linear element method for the Stokes problem. After
establishing a special quasi--orthogonality property for both the velocity and
the pressure in this saddle point problem, we introduce a new prolongation
operator to carry through the discrete reliability analysis for the error
estimator. We then use a specially defined interpolation operator to prove
that, up to oscillation, the error can be bounded by the approximation error
within a properly defined nonlinear approximate class. Finally, by introducing
a new parameter-dependent error estimator, we prove the convergence and
optimality estimates
Robust Preconditioners for Incompressible MHD Models
In this paper, we develop two classes of robust preconditioners for the
structure-preserving discretization of the incompressible magnetohydrodynamics
(MHD) system. By studying the well-posedness of the discrete system, we design
block preconditioners for them and carry out rigorous analysis on their
performance. We prove that such preconditioners are robust with respect to most
physical and discretization parameters. In our proof, we improve the existing
estimates of the block triangular preconditioners for saddle point problems by
removing the scaling parameters, which are usually difficult to choose in
practice. This new technique is not only applicable to the MHD system, but also
to other problems. Moreover, we prove that Krylov iterative methods with our
preconditioners preserve the divergence-free condition exactly, which
complements the structure-preserving discretization. Another feature is that we
can directly generalize this technique to other discretizations of the MHD
system. We also present preliminary numerical results to support the
theoretical results and demonstrate the robustness of the proposed
preconditioners
Microvariability Detection of Mrk 421
The BL Lac object Mrk 421 was observed in optical bands from 2009 April to
2012 May with the 1.0 m telescope at Weihai Observatory of Shandong University.
Microvariability was analysed by C and F tests, but no significant
microvariability was detected during our observations.Comment: 2 pages, 1 figur
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