64 research outputs found
The deal.II Library, Version 9.0
This paper provides an overview of the new features of the finite element library deal.II version 9.0
Dual weighted residual based error control for nonstationary convection-dominated equations: potential or ballast?
Even though substantial progress has been made in the numerical approximation
of convection-dominated problems, its major challenges remain in the scope of
current research. In particular, parameter robust a posteriori error estimates
for quantities of physical interest and adaptive mesh refinement strategies
with proved convergence are still missing. Here, we study numerically the
potential of the Dual Weighted Residual (DWR) approach applied to stabilized
finite element methods to further enhance the quality of approximations. The
impact of a strict application of the DWR methodology is particularly focused
rather than the reduction of computational costs for solving the dual problem
by interpolation or localization.Comment: arXiv admin note: text overlap with arXiv:1803.1064
A computational framework for the morpho-elastic development of molluskan shells by surface and volume growth
Mollusk shells are an ideal model system for understanding the morpho-elastic
basis of morphological evolution of invertebrates' exoskeletons. During the
formation of the shell, the mantle tissue secretes proteins and minerals that
calcify to form a new incremental layer of the exoskeleton. Most of the
existing literature on the morphology of mollusks is descriptive. The
mathematical understanding of the underlying coupling between pre-existing
shell morphology, de novo surface deposition and morpho-elastic volume growth
is at a nascent stage, primarily limited to reduced geometric representations.
Here, we propose a general, three-dimensional computational framework coupling
pre-existing morphology, incremental surface growth by accretion, and
morpho-elastic volume growth. We exercise this framework by applying it to
explain the stepwise morphogenesis of seashells during growth: new material
surfaces are laid down by accretive growth on the mantle whose form is
determined by its morpho-elastic growth. Calcification of the newest surfaces
extends the shell as well as creates a new scaffold that constrains the next
growth step. We study the effects of surface and volumetric growth rates, and
of previously deposited shell geometries on the resulting modes of mantle
deformation, and therefore of the developing shell's morphology. Connections
are made to a range of complex shells ornamentations.Comment: Main article is 20 pages long with 15 figures. Supplementary material
is 4 pages long with 6 figures and 6 attached movies. To be published in PLOS
Computational Biolog
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