相关论文: Nitsche Method for resolving boundary conditions o…
This article presents and analyzes a $p^{th}$-degree immersed finite element (IFE) method for elliptic interface problems with nonhomogeneous jump conditions. In this method, jump conditions are approximated optimally by basic IFE and…
Immersed finite element methods have been developed as a means to circumvent the costly mesh generation required in conventional finite element analysis. However, the numerical ill-conditioning of the resultant linear system of equations in…
We present a new finite element method, called $\phi$-FEM, to solve numerically elliptic partial differential equations with natural (Neumann or Robin) boundary conditions using simple computational grids, not fitted to the boundary of the…
In this paper, we introduce a novel unfitted finite element method to solve the quad-curl interface problem. We adapt Nitsche's method for curlcurl-conforming elements and double the degrees of freedom on interface elements. To ensure…
For most finite element simulations, boundary-conforming meshes have significant advantages in terms of accuracy or efficiency. This is particularly true for complex domains. However, with increased complexity of the domain, generating a…
An important step in shape optimization with partial differential equation constraints is to adapt the geometry during each optimization iteration. Common strategies are to employ mesh-deformation or re-meshing, where one or the other…
In many situations with finite element discretizations it is desirable or necessary to impose boundary or interface conditions not as essential conditions -- i.e. through the finite element space -- but through the variational formulation.…
This is the third paper on the study of gradient recovery for elliptic interface problem. In our previous works [H. Guo and X. Yang, 2016, arXiv:1607.05898 and {\it J. Comput. Phys.}, 338 (2017), 606--619], we developed {gradient recovery…
In this paper we consider a class of unfitted finite element methods for scalar elliptic problems. These so-called CutFEM methods use standard finite element spaces on a fixed unfitted triangulation combined with the Nitsche technique and a…
Interface problems have long been a major focus of scientific computing, leading to the development of various numerical methods. Traditional mesh-based methods often employ time-consuming body-fitted meshes with standard discretization…
The multimesh finite element method is a technique for solving partial differential equations on multiple non-matching meshes by enforcing interface conditions using Nitsche's method. Since the non-matching meshes can result in arbitrarily…
In this paper, an important discovery has been found for nonconforming immersed finite element (IFE) methods using the integral values on edges as degrees of freedom for solving elliptic interface problems. We show that those IFE methods…
In this paper, we extend the recently proposed extended scaled boundary finite element method (xSBFEM)~\cite{natarajansong2013} to study fracture parameters of interfacial cracks and cracks terminating at the interface. The approach is also…
Imposition of free slip boundary conditions in science and engineering simulations presents a challenge when the simulation domain is non-trivial. Inspired by recent progress in symbolic computation of discontinuous Galerkin finite element…
Acoustic wave propagation through a homogeneous material embedded in an unbounded medium can be formulated as a boundary integral equation and accurately solved with the boundary element method. The computational efficiency deteriorates at…
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…
The eXtreme Mesh deformation approach (X-MESH) is a new paradigm to follow sharp interfaces without remeshing and without changing the mesh topology. Even though the mesh does not change its topology, it can follow interfaces that do change…
This paper presents and analyzes an immersed finite element (IFE) method for solving Stokes interface problems with a piecewise constant viscosity coefficient that has a jump across the interface. In the method, the triangulation does not…
We present a projection-based numerical integration technique to deal with embedded interface in finite element (FE) framework. The element cut by an embedded interface is denoted as a cut cell. We recognize elemental matrices of a cut cell…
The multimesh finite element method enables the solution of partial differential equations on a computational mesh composed by multiple arbitrarily overlapping meshes. The discretization is based on a continuous--discontinuous function…