Related papers: Finite elements for the space approximation of a d…
Modeling of physical systems includes extensive use of software packages that implement the accurate finite element method for solving differential equations considered along with the appropriate initial and boundary conditions. When the…
In ecological studies of pattern formation, models of the competitive-diffusion type are generally singularly perturbed, and the numerical approximation of such models is challenging. In this paper, we present finite element discretization…
We introduce a surface finite element method for the numerical solution of Navier-Stokes equations on evolving surfaces with a prescribed deformation of the surface in normal direction. The method is based on approaches for the full surface…
We describe discretisations of the shallow water equations on the sphere using the framework of finite element exterior calculus, which are extensions of the mimetic finite difference framework presented in Ringler, Thuburn, Klemp, and…
A numerical method is proposed for a class of stochastic control problems including singular behavior. This method solves an infinite-dimensional linear program equivalent to the stochastic control problem using a finite element type…
As inelastic structures are ubiquitous in many engineering fields, a central task in computational mechanics is to develop accurate, robust and efficient tools for their analysis. Motivated by the poor performances exhibited by standard…
The paper studies a finite element method for computing transport and diffusion along evolving surfaces. The method does not require a parametrization of a surface or an extension of a PDE from a surface into a bulk outer domain. The…
An adaptive finite element method is presented for the elastic scattering of a time-harmonic plane wave by a periodic surface. First, the unbounded physical domain is truncated into a bounded computational domain by introducing the…
We study a finite element approximation of a coupled fluid-structure interaction consisting of a three-dimensional incompressible viscous fluid governed by the unsteady Stokes equations and a two-dimensional elastic plate. To avoid the use…
We develop a method to compute $H^2$-conforming finite element approximations in both two and three space dimensions using readily available finite element spaces. This is accomplished by deriving a novel, equivalent mixed variational…
This article surveys research on the application of compatible finite element methods to large scale atmosphere and ocean simulation. Compatible finite element methods extend Arakawa's C-grid finite difference scheme to the finite element…
This paper investigates the modeling of an important class of degradation data, which are collected from a spatial domain over time; for example, the surface quality degradation. Like many existing time-dependent stochastic degradation…
The paper introduces a new finite element numerical method for the solution of partial differential equations on evolving domains. The approach uses a completely Eulerian description of the domain motion. The physical domain is embedded in…
Finite element model updating of a structure made of linear elastic materials is based on the solution of a minimization problem. The goal is to find some unknown parameters of the finite element model (elastic moduli, mass densities,…
Phase transition problems on curved surfaces can lead to a panopticon of fascinating patterns. In this paper we consider finite element approximations of phase field models with a spatially inhomogeneous and anisotropic surface energy…
The paper introduces a finite element method for the incompressible Navier--Stokes equations posed on a closed surface $\Gamma\subset\R^3$. The method needs a shape regular tetrahedra mesh in $\mathbb{R}^3$ to discretize equations on the…
We present a finite element scheme for fractional diffusion problems with varying diffusivity and fractional order. We consider a symmetric integral form of these nonlocal equations defined on general geometries and in arbitrary bounded…
In this paper we present a new Eulerian finite element method for the discretization of scalar partial differential equations on evolving surfaces. In this method we use the restriction of standard space-time finite element spaces on a…
A high-order combined interpolation/finite element technique is developed for solving the coupled groundwater-surface water system that governs flows in karst aquifers. In the proposed high-order scheme we approximate the time derivative…
We present a space-time virtual element method for the discretization of the heat equation, which is defined on general prismatic meshes and variable degrees of accuracy. Strategies to handle efficiently the space-time mesh structure are…