899 research outputs found
Error estimates of a stabilized Lagrange-Galerkin scheme for the Navier-Stokes equations
Error estimates with optimal convergence orders are proved for a stabilized
Lagrange-Galerkin scheme for the Navier-Stokes equations. The scheme is a
combination of Lagrange-Galerkin method and Brezzi-Pitkaranta's stabilization
method. It maintains the advantages of both methods; (i) It is robust for
convection-dominated problems and the system of linear equations to be solved
is symmetric. (ii) Since the P1 finite element is employed for both velocity
and pressure, the number of degrees of freedom is much smaller than that of
other typical elements for the equations, e.g., P2/P1. Therefore, the scheme is
efficient especially for three-dimensional problems. The theoretical
convergence orders are recognized numerically by two- and three-dimensional
computations
Statistical properties of superflares on solar-type stars based on 1-min cadence data
We searched for superflares on solar-type stars using Kepler data with 1 min
sampling in order to detect superflares with short duration. We found 187
superflares on 23 solar-type stars whose bolometric energy ranges from the
order of erg to erg. Some superflares show multiple peaks
with the peak separation of the order of - seconds which is
comparable to the periods of quasi-periodic pulsations in solar and stellar
flares. Using these new data combined with the results from the data with 30
min sampling, we found the occurrence frequency () of superflares as a
function of flare energy () shows the power-law distribution () with for erg which is
consistent with the previous results. The average occurrence rate of
superflares with the energy of erg which is equivalent to X100 solar
flares is about once in 500-600 years. The upper limit of energy released by
superflares is basically comparable to a fraction of the magnetic energy stored
near starspots which is estimated from the photometry. We also found that the
duration of superflares () increases with the flare energy () as . This can be explained if we assume the time-scale of
flares is determined by the Alfvn time.Comment: Accepted for for publication in Earth, Planets and Spac
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