Related papers: Unique continuation for an elliptic interface prob…
We are concerned with the problem of determining the damping boundary coefficient appearing in a dissipative wave equation from a single boundary measurement. We prove that the uniqueness holds at the origin provided that the initial…
The phenomenon of arrest of an unstably-growing crack due to a curved weak interface is investigated. The weak interface can produce the deviation of the crack path, trapping the crack at the interface, leading to stable crack growth for…
This article considers the error analysis of finite element discretizations and adaptive mesh refinement procedures for nonlocal dynamic contact and friction, both in the domain and on the boundary. For a large class of parabolic…
We consider the finite difference discretization of isotropic elastic wave equations on nonuniform grids. The intended applications are seismic studies, where heterogeneity of the earth media can lead to severe oversampling for simulations…
We present stability and error analysis for algebraic flux correction schemes based on monolithic convex limiting. For a continuous finite element discretization of the time-dependent advection equation, we prove global-in-time existence…
We design and analyze a hybridized cut finite element method for elliptic interface problems. In this method very general meshes can be coupled over internal unfitted interfaces, through a skeletal variable, using a Nitsche type approach.…
This article presents an immersed virtual element method for solving a class of interface problems that combines the advantages of both body-fitted mesh methods and unfitted mesh methods. A background body-fitted mesh is generated…
Elliptic interface problems whose solutions are $C^0$ continuous have been well studied over the past two decades. The well-known numerical methods include the strongly stable generalized finite element method (SGFEM) and immersed FEM…
Trimming is a common operation in CAD, and, in its simplest formulation, consists in removing superfluous parts from a geometric entity described via splines (a spline patch). After trimming the geometric description of the patch remains…
This article presents results of further investigation of the problem of spurious interface fragmentation in the multiphase SPH. In order to remove arising instabilities, many authors introduced the artificial interface correction…
This paper presents a lowest-order immersed Raviart-Thomas mixed triangular finite element method for solving elliptic interface problems on unfitted meshes independent of the interface. In order to achieve the optimal convergence rates on…
In this paper, a shape optimization problem constrained by a random elliptic partial differential equation with a pure Neumann boundary is presented. The model is motivated by applications in interface identification, where we assume…
A variational model for describing the morphology of two-phase continua by allowing for the interplay between coherent and incoherent interfaces is introduced. Coherent interfaces are characterized by the microscopical arrangement of atoms…
For elliptic interface problems in two- and three-dimensions, this paper establishes a priori error estimates for Crouzeix-Raviart nonconforming, Raviart-Thomas mixed, and discontinuous Galerkin finite element approximations. These…
We approximate an elliptic problem with oscillatory coefficients using a problem of the same type, but with constant coefficients. We deliberately take an engineering perspective, where the information on the oscillatory coefficients in the…
The paper introduces an adaptive version of the stabilized Trace Finite Element Method (TraceFEM) designed to solve low-regularity elliptic problems on level-set surfaces using a shape-regular bulk mesh in the embedding space. Two…
In this note we study periodic homogenization of Dirichlet problem for divergence type elliptic systems when both the coefficients and the boundary data are oscillating. One of the key difficulties here is the determination of the fixed…
The aim of this note is to review some recent developments on the regularity theory for the stationary and parabolic obstacle problems. After a general overview, we present some recent results on the structure of singular free boundary…
We study the generalized finite element methods (GFEMs) for the second-order elliptic eigenvalue problem with an interface in 1D. The linear stable generalized finite element methods (SGFEM) were recently developed for the elliptic source…
The dynamics of singularity formation on the interface between two ideal fluids is studied for the Kelvin-Helmholtz instability development within the Hamiltonian formalism. It is shown that the equations of motion derived in the small…