Energy-corrected FEM and explicit time-stepping for parabolic problems

The presence of corners in the computational domain, in general, reduces the regularity of solutions of parabolic problems and diminishes the convergence properties of the finite element approximation introducing a so-called "pollution effect". Standard remedies based on mesh refinement around the singular corner result in very restrictive stability requirements on the time-step size when explicit time integration is applied. In this article, we introduce and analyse the energy-corrected finite element method for parabolic problems, which works on quasi-uniform meshes, and, based on it, create fast explicit time discretisation. We illustrate these results with extensive numerical investigations not only confirming the theoretical results but also showing the flexibility of the method, which can be applied in the presence of multiple singular corners and a three-dimensional setting. We also propose a fast explicit time-stepping scheme based on a piecewise cubic energy-corrected discretisation in space completed with mass-lumping techniques and numerically verify its efficiency

Nambu-Goto string action with Gauss-Bonnet term

We examine the relativistic Nambu-Goto model with Gauss-Bonnet boundary term added to the action integral. The system is analysed using an invariant representation of dynamical string degrees of freedom by complex Liouville fields. The solutions of classical equations of motion for open strings are described.Comment: 9 pages, late

Three-body forces from a classical nonlinear field

Forces in the systems of two opposite sign and three identical charges coupled to the dynamical scalar field of the signum-Gordon model are investigated. Three-body force is present, and the exact formula for it is found. Flipping the sign of one of the two charges changes not only the sign but also the magnitude of the force. Both effects are due to nonlinearity of the field equation.Comment: 12 pages, 2 figure

SALT observations of southern post-novae

We report on recent optical observations of the stellar and the nebular remnants of 22 southern post-novae. In this study, for each of our targets, we obtained and analysed long-slit spectra in the spectral range 3500-6600 A and in H$\alpha$+NII narrow-band images. The changes in the emission lines' equivalent widths with the time since the outburst agree with earlier published results of other authors. We estimated an average value $\alpha$=2.37 for the exponent of the power law fitted to the post-novae continua. Our observations clearly show the two-component structure of the V842 Cen expanding nebulae, owing to the different velocities of the ejected matter. We discovered an expanding shell around V382 Vel with an outer diameter of about 12 arcsec.Comment: 24 pages, 19 figures, A&A accepte