Effects of Coronal Density and Magnetic Field Distributions on a Global Solar EUV Wave

We investigate a global extreme-ultraviolet (EUV) wave associated with a coronal mass ejection (CME)-driven shock on 2017 September 10. The EUV wave is transmitted by north- and south-polar coronal holes (CHs), which is observed by the Solar Dynamics Observatory (SDO) and Solar Terrestrial Relations Observatory A (STEREO-A) from opposite sides of the Sun. We obtain key findings on how the EUV wave interacts with multiple coronal structures, and on its connection with the CME-driven shock: (1) the transmitted EUV wave is still connected with the shock that is incurvated to the Sun, after the shock has reached the opposite side of the eruption; (2) the south CH transmitted EUV wave is accelerated inside an on-disk, low-density region with closed magnetic fields, which implies that an EUV wave can be accelerated in both open and closed magnetic field regions; (3) part of the primary EUV wavefront turns around a bright point (BP) with a bipolar magnetic structure when it approaches a dim, low-density filament channel near the BP; (4) the primary EUV wave is diffused and apparently halted near the boundaries of remote active regions (ARs) that are far from the eruption, and no obvious AR related secondary waves are detected; (5) the EUV wave extends to an unprecedented scale of ~360{\deg} in latitudes, which is attributed to the polar CH transmission. These results provide insights into the effects of coronal density and magnetic field distributions on the evolution of an EUV wave, and into the connection between the EUV wave and the associated CME-driven shock.Comment: 16 pages, 8 figures, and 3 animations available at http://doi.org/10.13140/RG.2.2.12408.29442 , http://doi.org/10.13140/RG.2.2.25830.06723 , and http://doi.org/10.13140/RG.2.2.19119.18088 ; published in Ap

An adaptive finite element method for distributed elliptic optimal control problems with variable energy regularization

We analyze the finite element discretization of distributed elliptic optimal control problems with variable energy regularization, where the usual $L^2(\Omega)$ norm regularization term with a constant regularization parameter $\varrho$ is replaced by a suitable representation of the energy norm in $H^{-1}(\Omega)$ involving a variable, mesh-dependent regularization parameter $\varrho(x)$. It turns out that the error between the computed finite element state $\widetilde{u}_{\varrho h}$ and the desired state $\bar{u}$ (target) is optimal in the $L^2(\Omega)$ norm provided that $\varrho(x)$ behaves like the local mesh size squared. This is especially important when adaptive meshes are used in order to approximate discontinuous target functions. The adaptive scheme can be driven by the computable and localizable error norm $\| \widetilde{u}_{\varrho h} - \bar{u}\|_{L^2(\Omega)}$ between the finite element state $\widetilde{u}_{\varrho h}$ and the target $\bar{u}$. The numerical results not only illustrate our theoretical findings, but also show that the iterative solvers for the discretized reduced optimality system are very efficient and robust