Related papers: A fictitious domain approach with distributed Lagr…
In this note we design a cut finite element method for a low order divergence free element applied to a boundary value problem subject to Stokes' equations. For the imposition of Dirichlet boundary conditions we consider either Nitsche's…
We present a novel formulation for parametric finite element methods to approximate two-phase Stokes flow. The new formulation is based on the classical Stokes equation in the bulk and a novel choice of interface conditions with additional…
The present paper deals with the interior solid-fluid interaction problem in harmonic regime with randomly perturbed boundaries. Analysis of the shape derivative and shape Hessian of vector- and tensor-valued functions is provided. Moments…
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…
We present a space-time continuous-Galerkin finite element method for solving incompressible Navier-Stokes equations. To ensure stability of the discrete variational problem, we apply ideas from the variational multi-scale method. The…
The stable operation of gas networks is an important optimization target. While for this task commonly finite volume methods are used, we introduce a new finite difference approach. With a summation by part formulation for the spatial…
We present a parallel time-stepping method for fluid-structure interactions. The interaction between the incompressible Navier-Stokes equations and a hyperelastic solid is formulated in a fully monolithic framework. Discretization in space…
For problems involving large deformations of thin structures, simulating fluid-structure interaction (FSI) remains challenging largely due to the need to balance computational feasibility, efficiency, and solution accuracy. Overlapping…
We present approaches for the study of fluid-structure interactions subject to thermal fluctuations. A mixed mechanical description is utilized combining Eulerian and Lagrangian reference frames. We establish general conditions for…
In this work we develop an a posteriori error analysis of a conforming mixed finite element method for solving the coupled problem arising in the interaction between a free fluid and a fluid in a poroelastic medium on isotropic meshes in…
We develop a space-time mortar mixed finite element method for parabolic problems. The domain is decomposed into a union of subdomains discretized with non-matching spatial grids and asynchronous time steps. The method is based on a…
Isogeometrically enriched finite elements offer efficient localized isogeometric analysis (IGA) enrichment for numerical simulations involving large computational domains. This is achieved by employing surface enriched elements to interface…
We investigate a fluid-structure interaction system in which the dynamics of the fluid is described by the compressible Navier-Stokes equations, while the elastic structure is modeled by a damped plate equation. The fluid evolves in a…
An iterative optimization approach that simultaneously minimizes the energy and optimizes the Lagrange multipliers enforcing desired constraints is presented. The method is tested on previously established benchmark systems and it is proved…
Over the past few decades, there has been a rapid improvement in computational power as well as techniques to simulate the real world phenomenon which has enabled us to understand the physics and develop new systems which outperform the…
This paper develops the a priori analysis of a mixed finite element method for the filtration of an incompressible fluid through a non-deformable saturated porous medium with heterogeneous permeability. Flows are governed by the…
The pseudopotential model within the Lattice Boltzmann Method (LBM) framework has emerged as a prominent approach in computational fluid dynamics due to its dual strengths in physical intuitiveness and computational tractability. However,…
This paper presents a numerical method for the simulation of multiscale materials composed of an elastic matrix and slender active inclusions. The setting is motivated by the modeling of vascularized tissues and by problems arising in the…
We present a loosely-coupled partitioned scheme for a benchmark problem in fluid-composite structure interaction. The benchmark problem proposed here consists of an incompressible, viscous fluid interacting with a composite structure that…
A non-overlapping domain decomposition algorithm is proposed to solve the linear system arising from mixed finite element approximation of incompressible Stokes equations. A continuous finite element space for the pressure is used. In the…