Related papers: An Arbitrary-Order Moving-Mesh Finite Element Algo…
We develop a finite element method for the Laplace-Beltrami operator on a surface with boundary and nonhomogeneous Dirichlet boundary conditions. The method is based on a triangulation of the surface and the boundary conditions are enforced…
In the present work, we examine and analyze an hp-version interior penalty discontinuous Galerkin finite element method for the numerical approximation of a steady fluid system on computational meshes consisting of polytopic elements on the…
This paper presents a high-order method for solving an interface problem for the Poisson equation on embedded meshes through a coupled finite element and integral equation approach. The method is capable of handling homogeneous or…
We develop a parametric cut finite element method for elliptic boundary value problems with corner singularities where we have weighted control of higher order derivatives of the solution to a neighborhood of a point at the boundary. Our…
A high-order space-time flux reconstruction (FR) method has been developed to solve conservation laws on moving domains. In the space-time framework, the moving domain simulation is similar to that on a stationary domain, except that the…
In this work a finite element simulation of the motion of a rigid body in a fluid, with free surface, is described. A completely general referential description (of which both Lagrangian and Eulerian descriptions are special cases) of an…
In this paper we propose a finite element method for solving elliptic equations with the observational Dirichlet boundary data which may subject to random noises. The method is based on the weak formulation of Lagrangian multiplier. We show…
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…
In this paper, we propose a mass conservative semi-Lagrangian finite difference scheme for multi-dimensional problems without dimensional splitting. The semi-Lagrangian scheme, based on tracing characteristics backward in time from grid…
We introduce a robust first order accurate meshfree method to numerically solve time-dependent nonlinear conservation laws. The main contribution of this work is the meshfree construction of first order consistent summation by parts…
In this paper, we propose a linear and monolithic finite element method for the approximation of an incompressible viscous fluid interacting with an elastic and deforming plate. We use the arbitrary Lagrangian-Eulerian (ALE) approach that…
An isogeometric boundary element method (BEM) is presented to solve scattering problems in an isotropic homogeneous medium. We consider wave problems governed by the scalar wave equation as in acoustics and the Lam\'e-Navier equations for…
We present a new framework for expressing finite element methods on multiple intersecting meshes: multimesh finite element methods. The framework enables the use of separate meshes to discretize parts of a computational domain that are…
We study finite element approximations of second-order elliptic problems with measure-valued right-hand sides supported on lower-dimensional sets. The exact solution generally lacks $H^1$-regularity due to the source singularity, which…
The accuracy of finite element solutions is closely tied to the mesh quality. In particular, geometrically nonlinear problems involving large and strongly localized deformations often result in prohibitively large element distortions. In…
We propose an open-boundary molecular dynamics method in which an atomistic system is in contact with an infinite particle reservoir at constant temperature, volume and chemical potential. In practice, following the Hamiltonian adaptive…
We consider the evolution of an incompressible two-dimensional perfect fluid as the boundary of its domain is deformed in a prescribed fashion. The flow is taken to be initially steady, and the boundary deformation is assumed to be slow…
This work proposes a novel variational approximation of partial differential equations on moving geometries determined by explicit boundary representations. The benefits of the proposed formulation are the ability to handle large…
We present a cut finite element method for the heat equation on two overlapping meshes: a stationary background mesh and an overlapping mesh that moves around inside/"on top" of it. Here the overlapping mesh is prescribed a simple…
In this paper, we propose and analyze a linear second-order numerical method for solving the Allen-Cahn equation with a general mobility. The proposed fully-discrete scheme is carefully constructed based on the combination of first and…