Related papers: Simplex space-time meshes in engineering applicati…
Both non-Abelian gauge fields and minimally interacting massless matter fields are localized on a domain wall in the five-dimensional spacetime. Field-dependent gauge coupling naturally gives a position-dependent coupling to localize…
We propose, analyze, and test new robust iterative solvers for systems of linear algebraic equations arising from the space-time finite element discretization of reduced optimality systems defining the approximate solution of hyperbolic…
Two non-overlapping domain decomposition methods are presented for the mixed finite element formulation of linear elasticity with weakly enforced stress symmetry. The methods utilize either displacement or normal stress Lagrange multiplier…
Unfitted (also known as embedded or immersed) finite element approximations of partial differential equations are very attractive because they have much lower geometrical requirements than standard body-fitted formulations. These schemes do…
In this paper, we present and validate a simple adaptive surface remeshing technique to transfer history dependent variables from an old distorting mesh to a new mesh during finite element simulations of elastic surface deformation. This…
We develop a finite element method for the Laplace--Beltrami operator on a surface described by a set of patchwise parametrizations. The patches provide a partition of the surface and each patch is the image by a diffeomorphism of a…
Mechanical metamaterials leverage geometric design to achieve unconventional properties, such as high strength at low density, efficient wave guiding, and complex shape morphing. The ability to control shape changes builds on the complex…
This work provides an efficient virtual element scheme for the modeling of nonlinear elastodynamics undergoing large deformations. The virtual element method (VEM) has been applied to various engineering problems such as elasto-plasticity,…
We develop a new finite element method for solving planar elasticity problems involving of heterogeneous materials with a mesh not necessarily aligning with the interface of the materials. This method is based on the `broken'…
We present a monolithic $hp$ space-time multigrid method for tensor-product space-time finite element discretizations of the Stokes equations. Geometric and polynomial coarsening of the space-time mesh is performed, and the entire algorithm…
We examine the Euler equations within a simply-connected bounded domain. The dynamics of a single point vortex are governed by a Hamiltonian system, with most of its energy levels corresponding to time-periodic motion. We show that for the…
We consider so-called branched transport and variants thereof in two space dimensions. In these models one seeks an optimal transportation network for a given mass transportation task. In two space dimensions, they are closely connected to…
An arbitrary Lagrangian--Eulerian finite element method and numerical implementation for curved and deforming lipid membranes is presented here. The membrane surface is endowed with a mesh whose in-plane motion need not depend on the…
Recovered finite element methods (R-FEM) have been recently introduced for meshes consisting of simplicial and/or box-type meshes. Here, utilising the flexibility of R-FEM framework, we extend their definition on polygonal and polyhedral…
Standard finite element methods employ an element-wise assembly strategy. The element's contribution to the system matrix is formed by a loop over quadrature points. This concept is also used in fictitious domain methods, which perform…
Geometric decomposition is a widely used tool for constructing local bases for finite element spaces. For finite element spaces of differential forms on simplicial meshes, Arnold, Falk, and Winther showed that geometric decompositions can…
The concept of the random discretization of the space-time is suggested. It is the way to consistent compatible synthesis of quantum and relativistic principles and principle of geometrization. The basic idea of this concept is physical…
This note proposes embedding a time dependent PDE into a convection-diffusion type PDE (in one space dimension higher) with singularity, for which two discretization schemes, the classical streamline-diffusion and the EAFE (edge average…
We introduce an unfitted finite element method with Lagrange-multipliers to study an Eulerian time stepping scheme for moving domain problems applied to a model problem where the domain motion is implicit to the problem. We consider a…
Internal interfaces in a domain could exist as a material defect or they can appear due to propagations of cracks. Discretization of such geometries and solution of the contact problem on the internal interfaces can be computationally…