Related papers: Simulation of constrained elastic curves and appli…
The article addresses the mathematical modeling of the folding of a thin elastic sheet along a prescribed curved arc. A rigorous model reduction from a general hyperelastic material description is carried out under appropriate scaling…
We study a higher-order surface finite element (SFEM) penalty-based discretization of the tangential surface Stokes problem. Several discrete formulations are investigated which are equivalent in the continuous setting. The impact of the…
Density profiles are the most common measure of inhomogeneous structure in confined fluids, but their connection to transport coefficients is poorly understood. We explore via simulation how tuning particle-wall interactions to flatten or…
We consider numerical simulation of the isotropic elastic wave equations arising from seismic applications with non-trivial land topography. The more flexible finite element method is applied to the shallow region of the simulation domain…
We investigate a finite element discretization of an elastic bending-plate model with an effective prestrain. The model has been obtained via homogenization and dimension reduction by B\"onlein at al. (2023). Its energy functional is the…
We develop two adaptive discretization algorithms for convex semi-infinite optimization, which terminate after finitely many iterations at approximate solutions of arbitrary precision. In particular, they terminate at a feasible point of…
In the context of mathematical modeling, it is sometimes convenient to integrate models of different nature. These types of combinations, however, might entail difficulties even when individual models are well-understood, particularly in…
We consider a numerical scheme for the approximation of a system that couples the evolution of a two--dimensional hypersurface to a reaction--diffusion equation on the surface. The surfaces are assumed to be graphs and evolve according to…
We provide a rigorous justification of the classical linearization approach in plasticity. By taking the small-deformations limit, we prove via \Gamma-convergence for rate-independent processes that energetic solutions of the quasi-static…
We present fully analytical solutions for the deformation of a stretched soft substrate due to the static wetting of a large liquid droplet, and compare our solutions to recently published experiments (Xu et al, Soft Matter 2018). Following…
We study the systematic numerical approximation of a class of Allen-Cahn type problems modeling the motion of phase interfaces. The common feature of these models is an underlying gradient flow structure which gives rise to a decay of an…
This work concerns the numerical analysis of the linear elasticity problem with a Robin boundary condition on a smooth domain. A finite element discretization is presented using high-order curved meshes in order to accurately discretize the…
The mollified uniform distribution is rediscovered, which constitutes a ``soft'' version of the continuous uniform distribution. Important stochastic properties are presented and used to demonstrate potential fields of applications. For…
High-order spatial discretisations and full discretisations of parabolic partial differential equations on evolving surfaces are studied. We prove convergence of the high-order evolving surface finite element method, by showing high-order…
The nonlinear spaces of shapes (unparameterized immersed curves or submanifolds) are of interest for many applications in image analysis, such as the identification of shapes that are similar modulo the action of some group. In this paper…
In the discretization of differential problems on complex geometrical domains, discretization methods based on polygonal and polyhedral elements are powerful tools. Adaptive mesh refinement for such kind of problems is very useful as well…
We study a mathematical model for deformation of glued elastic bodies in 2D or 3D, which is a linear elasticity system with adhesive force on the glued surface. We reveal a variational structure of the model and prove the unique existence…
Consider the following variational problem: among all curves in $\mathbb{R}^n$ of fixed length with prescribed end points and prescribed tangents at the end points, minimise the $L^\infty$-norm of the curvature. We show that the solutions…
The second gradient model of poromechanics, introduced in Part I, is here linearized in the neighborhood of a prestressed reference configuration to be applied to the one-dimensional consolidation problem originally considered by Terzaghi…
We propose an extension of the discretization approaches for multilayer shallow water models, aimed at making them more flexible and efficient for realistic applications to coastal flows. A novel discretization approach is proposed, in…