Related papers: Compatible finite element methods for geophysical …
The simulation of heat flow through heterogeneous material is important for the design of structural and electronic components. Classical analytical solutions to the heat equation PDE are not known for many such domains, even those having…
A port-Hamiltonian (pH) system formulation is a geometrical notion used to formulate conservation laws for various physical systems. The distributed parameter port-Hamiltonian formulation models infinite dimensional Hamiltonian dynamical…
We propose a new unfitted finite element method for simulation of two-phase flows in presence of insoluble surfactant. The key features of the method are 1) discrete conservation of surfactant mass; 2) the possibility of having meshes that…
Finite element methods provide accurate and efficient methods for the numerical solution of partial differential equations by means of restricting variational problems to finite-dimensional approximating spaces. However, they do not…
In this paper we present PDE and finite element analyses for a system of partial differential equations (PDEs) consisting of the Darcy equation and the Cahn-Hilliard equation, which arises as a diffuse interface model for the two phase…
We develop stochastic mixed finite element methods for spatially adaptive simulations of fluid-structure interactions when subject to thermal fluctuations. To account for thermal fluctuations, we introduce a discrete fluctuation-dissipation…
This paper presents a mixed finite element framework for coupled hydro-mechanical-chemical processes in heterogeneous porous media. The framework combines two types of locally conservative discretization schemes: (1) an enriched Galerkin…
With this contribution, we give a complete and comprehensive framework for modeling the dynamics of complex mechanical structures as port-Hamiltonian systems. This is motivated by research on the potential of lightweight construction using…
In this paper, we define new unfitted finite element methods for numerically approximating the solution of surface partial differential equations using bulk finite elements. The key idea is that the $n$-dimensional hypersurface, $\Gamma…
Energy-preserving numerical methods for solving the Hodge wave equation is developed in this paper. Based on the de Rham complex, the Hodge wave equation can be formulated as a first-order system and mixed finite element methods using…
Rigorous computer simulations of propagating electromagnetic fields have become an important tool for optical metrology and design of nanostructured optical components. A vectorial finite element method (FEM) is a good choice for an…
Two de Rham complex sequences of the finite element spaces are introduced for weak finite element functions and weak derivatives developed in the weak Galerkin (WG) finite element methods on general polyhedral elements. One of the sequences…
In this paper, a symmetrized two-scale finite element method is proposed for a class of partial differential equations with symmetric solutions. With this method, the finite element approximation on a fine tensor product grid is reduced to…
In order to learn distributed port-Hamiltonian systems (dPHS) using Gaussian processes (GPs), the partitioned finite element method (PFEM) is combined with the Gp-dPHS method. By following a late lumping approach, the discretization of the…
The finite element simulation of dynamic wetting phenomena, requiring the computation of flow in a domain confined by intersecting a liquid-fluid free surface and a liquid-solid interface, with the three-phase contact line moving across the…
This article investigates a space-time differential model related to the degradation of stone artifacts caused by exposure to air and atmospheric agents, which specifically lead to the accumulation of salt crystals in the material. A…
In this article, a new generic higher-order finite-element framework for massively parallel simulations is presented. The modular software architecture is carefully designed to exploit the resources of modern and future supercomputers.…
In this paper we describe a computational model for the simulation of fluid-structure interaction problems based on a fictitious domain approach. We summarize the results presented over the last years when our research evolved from the…
The moist shallow water equations offer a promising route for advancing understanding of the coupling of physical parametrisations and dynamics in numerical atmospheric models, an issue known as 'physics-dynamics coupling'. Without moist…
This paper presents a structure-preserving spatial discretization method for distributed parameter port-Hamiltonian systems. The class of considered systems are hyperbolic systems of two conservation laws in arbitrary spatial dimension and…