相关论文: A Mini Immersed Finite Element Method for Two-Phas…

Steady and unsteady Poisson and Stokes equations are solved using mesh dependent Finite Element Method and meshless Radial Basis Function Collocation Method to compare the performances of these two numerical techniques across several…

We present a Cartesian cut-cell finite-volume method for sharp-interface two-phase diffusion problems in static geometries. The formulation follows a two-fluid approach: independent diffusion equations are discretized in each phase on a…

Multiscale Finite Element Methods (MsFEMs) are now well-established finite element type approaches dedicated to multiscale problems. They first compute local, oscillatory, problem-dependent basis functions that generate a suitable…

Fourier solvers have become efficient tools to establish structure-property relations in heterogeneous materials. Introduced as an alternative to the Finite Element (FE) method, they are based on fixed-point solutions of the…

We present the implementation of a solution scheme for fluid-structure interaction problems via the finite element software library deal.II. The solution scheme is an immersed finite element method in which two independent discretizations…

It has been noted that the traditional scaling argument cannot be directly applied to the error analysis of immersed finite elements (IFE) because, in general, the spaces on the reference element associated with the IFE spaces on different…

In this paper we apply the recently developed mimetic discretization method to the mixed formulation of the Stokes problem in terms of vorticity, velocity and pressure. The mimetic discretization presented in this paper and in [50] is a…

This work considers a Stokes flow in a deformable fracture interacting with a linear elastic medium. To this end, we employ a phase-field model to approximate the crack dynamics. Phase-field methods belong to interface-capturing approaches…

We consider the numerical approximation of a sharp-interface model for two-phase flow, which is given by the incompressible Navier-Stokes equations in the bulk domain together with the classical interface conditions on the interface. We…

In this work, we present an adaptive unfitted finite element scheme that combines the aggregated finite element method with parallel adaptive mesh refinement. We introduce a novel scalable distributed-memory implementation of the resulting…

We introduce new control-volume finite-element discretization schemes suitable for solving the Stokes problem. Within a common framework, we present different approaches for constructing such schemes. The first and most established strategy…

An important requirement in the standard finite element method (FEM) is that all elements in the underlying mesh must be tangle-free i.e., the Jacobian must be positive throughout each element. To relax this requirement, an isoparametric…

This work develops and analyzes a variational-monolithic unfitted finite element formulation of a linear fluid-structure interaction problem in Eulerian coordinates with a fixed interface. The overall discretization is based on a backward…

This paper develops divergence-free mixed finite element methods for the Stokes equation. Using H(div)-conforming velocities and discontinuous pressures ensures the inf-sup condition for the velocity--pressure pair and yields pointwise…

We present an immersed interface method for the vorticity-velocity form of the 2D Navier Stokes equations that directly addresses challenges posed by multiply connected domains, nonconvex obstacles, and the calculation of force…

We consider within a finite element approach the usage of different adaptively refined meshes for different variables in systems of nonlinear, time-depended PDEs. To resolve different solution behaviours of these variables, the meshes can…

High-order numerical methods for solving elliptic equations over arbitrary domains typically require specialized machinery, such as high-quality conforming grids for finite elements method, and quadrature rules for boundary integral…

Piecewise divergence-free nonconforming virtual elements are designed for Stokes problem in any dimensions. After introducing a local energy projector based on the Stokes problem and the stabilization, a divergence-free nonconforming…

In this paper we present a fully-coupled, two-scale homogenization method for dynamic loading in the spirit of FE$^2$ methods. The framework considers the balance of linear momentum including inertia at the microscale to capture possible…

Fluid-solid interfacial free energy (IFE) is a fundamental parameter influencing wetting behaviors, which play a crucial role across a broad range of industrial applications. Obtaining reliable data for fluid-solid IFE remains challenging…