Robust Numerical Methods for Singularly Perturbed Differential Equations--Supplements

The second edition of the book "Roos, Stynes, Tobiska -- Robust Numerical Methods for Singularly Perturbed Differential Equations" appeared many years ago and was for many years a reliable guide into the world of numerical methods for singularly perturbed problems. Since then many new results came into the game, we present some selected ones and the related sources.Comment: arXiv admin note: text overlap with arXiv:1909.0827

Vandalism as a Symbolic Act in Free Zones

The concept of vandalism is analyzed as a symbolic act. An analysis of vandalism from a situational-positivistic, or a motivational-psychological, approach hardly gives an understanding of vandalism as a meaningful individual and social act. A humanistic and cultural perspective can supply ways to understand a nonprescribed behavior such as vandalism. The original meaning of vandalism is plundering and laying waste of a civilization's symbols and environment. This appropriation of physical environment also occurs in the industrialized societies' urban environment and then often is perceived as motiveless. "Free zones" develop in societies where norms and obligations are neutralized. Vandalism is nonprescribed in that it appears in these free zones where norms, obligations, utility, and common sense are switched off. The environment is "marked" by damaging or destroying objects to change the message of the physical milieu. Vandalism is a gesture of "negative honor," which reflects a complex of feelings. Vandalism comprises two sides of an autonomy problem: to be isolated from an unwanted membership (juvenile vandalism) and to be free of an unwanted outside position (adult vandalism). An essential question is which methodological and theoretical concepts a researcher in the social sciences should use to discover the rationality of vandalism and to make it comprehensible

Remarks on boundary layers in singularly perturbed Caputo fractional boundary value problems

Almost nothing is known about the layer structure of solutions to singularly perturbed Caputo fractional boundary value problems. We discuss simple convection-diffusion and reaction-diffusion problems

Error estimates for linear finite elements on Bakhvalov-type meshes

summary:For convection-diffusion problems with exponential layers, optimal error estimates for linear finite elements on Shishkin-type meshes are known. We present the first optimal convergence result in an energy norm for a Bakhvalov-type mesh