Related papers: A Smooth Partition of Unity Finite Element Method …
In this paper, we propose and analyze a finite element discretization for the computation of fractional minimal graphs of order~$s \in (0,1/2)$ on a bounded domain $\Omega$. Such a Plateau problem of order $s$ can be reinterpreted as a…
We numerically investigate magnetization, pinning, ordering, and dynamics of vortices interacting with pinning arrangements which have a density gradient. We focus on conformal crystal structures obtained by conformally transforming a…
To obtain the highest confidence on the correction of numerical simulation programs for the resolution of Partial Differential Equations (PDEs), one has to formalize the mathematical notions and results that allow to establish the soundness…
We propose a new discrete FFT-based method for computational homogenization of micromechanics on a regular grid that is simple, fast and robust. The discretization scheme is based on a tetrahedral stencil that displays three crucial…
In this thesis we develop a stabilised finite element method for solving the equations of poroelasticity to enable solving complex models of biological tissues such as the human lungs. For the proposed numerical scheme, we use the lowest…
In this work we investigate the scaling properties of quasiparticles of Pnictide with "half-Dirac" node under magnetic field in vortex state. By computing the density of states, we aim to find in vortex state the form of non-Simon-Lee…
We develop a finite element method for the vector Laplacian based on the covariant derivative of tangential vector fields on surfaces embedded in $\mathbb{R}^3$. Closely related operators arise in models of flow on surfaces as well as…
We derive the equations of motion for a planar rigid body of circular shape moving in a 2D perfect fluid with point vortices using symplectic reduction by stages. After formulating the theory as a mechanical system on a configuration space…
This paper considers the discretization of the time-dependent Navier-Stokes equations with the family of inf-sup stabilized Scott-Vogelius pairs recently introduced in [John/Li/Merdon/Rui, arXiv:2206.01242, 2022] for the Stokes problem.…
We consider a system of nonlinear partial differential equations describing the motion of an incompressible chemically reacting generalized Newtonian fluid in three space dimensions. The governing system consists of a steady…
In many applications the accurate representation of the computational domain is a key factor to obtain reliable and effective numerical solutions. Curved interfaces, which might be internal, related to physical data, or portions of the…
This article presents a new finite element method for convection-diffusion equations by enhancing the continuous finite element space with a flux space for flux approximations that preserve the important mass conservation locally on each…
This work develops an epsilon-uniform finite element method for singularly perturbed boundary value problems. A surprising and remarkable observation is illustrated: By moving one node arbitrarily in between its adjacent nodes, the new…
Symmetry-preserving (mimetic) discretization aims to preserve certain properties of a continuous differential operator in its discrete counterpart. For these discretizations, stability and (discrete) conservation of mass, momentum and…
The goal of this paper is to present a formalism that allows to handle four-fermion effective theories at finite temperature and density in curved space. The formalism is based on the use of the effective action and zeta function…
We develop a micromorphic-based approach for finite element stabilization of reaction-convection-diffusion equations, by gradient enhancement of the field of interest via introducing an auxiliary variable. The well-posedness of the…
We introduce an efficient finite-element approach for large-scale real-space pseudopotential density functional theory (DFT) calculations incorporating noncollinear magnetism and spin-orbit coupling. The approach, implemented within the…
In this article, we analyse a stabilised equal-order finite element approximation for the Stokes equations on anisotropic meshes. In particular, we allow arbitrary anisotropies in a sub-domain, for example along the boundary of the domain,…
We introduce a new formulation for the finite element immersed boundary method which makes use of a distributed Lagrange multiplier. We prove that a full discretization of our model, based on a semi-implicit time advancing scheme, is…
A variational method is used to derive a self-consistent macro-particle model for relativistic electromagnetic kinetic plasma simulations. Extending earlier work [E. G. Evstatiev and B. A. Shadwick, J. Comput. Phys., vol. 245, pp. 376-398,…