Related papers: Deep unfitted Nitsche method for elliptic interfac…
We propose a multiscale method for elliptic problems on complex domains, e.g. domains with cracks or complicated boundary. For local singularities this paper also offers a discrete alternative to enrichment techniques such as XFEM. We…
We consider numerical solution of elliptic problems with heterogeneous diffusion coefficients containing thin highly conductive structures. Such problems arise e.g. in fractured porous media, reinforced materials, and electric circuits. The…
We survey the Nitsche's master-slave finite element method for elastic contact problems analysed in [2]. The main steps of the error analysis are recalled and numerical benchmark computations are presented.
In this paper, a meshfree method using the deep neural network (DNN) approach is developed for solving two kinds of dynamic two-phase interface problems governed by different dynamic partial differential equations on either side of the…
We extend a distributed finite element method built upon model order reduction to arbitrary polynomial degree using a hybrid Nitsche scheme. The new method considerably simplifies the transformation of the finite element system to the…
Interface problems depict many fundamental physical phenomena and widely apply in the engineering. However, it is challenging to develop efficient fully decoupled numerical methods for solving degenerate interface problems in which the…
The elliptic interface problems with discontinuous and high-contrast coefficients appear in many applications and often lead to huge condition numbers of the corresponding linear systems. Thus, it is highly desired to construct high order…
In this paper, we present an immersed weak Galerkin method for solving second-order elliptic interface problems. The proposed method does not require the meshes to be aligned with the interface. Consequently, uniform Cartesian meshes can be…
This paper proposes a deep-learning-based domain decomposition method (DeepDDM), which leverages deep neural networks (DNN) to discretize the subproblems divided by domain decomposition methods (DDM) for solving partial differential…
We propose a boundary-corrected weak Galerkin mixed finite element method for solving elliptic interface problems in 2D domains with curved interfaces. The method is formulated on body-fitted polygonal meshes, where interface edges are…
We study an elliptic interface problem with discontinuous diffusion coefficients on unfitted meshes using the CutFEM method. Our main contribution is the reconstruction of conservative fluxes from the CutFEM solution and their use in a…
In the context of unfitted finite element discretizations the realization of high order methods is challenging due to the fact that the geometry approximation has to be sufficiently accurate. We consider a new unfitted finite element method…
We study an optimal control problem under uncertainty, where the target function is the solution of an elliptic partial differential equation with random coefficients, steered by a control function. The robust formulation of the…
By integrating physics-informed neural network (PINN) techniques with domain decomposition method, a deep domain decomposition method is presented for solving elliptic variational inequality problems. Based on the Ritz variation method, the…
We propose a discontinuous Galerkin(DG) method to approximate the elliptic interface problem on unfitted mesh using a new approximation space. The approximation space is constructed by patch reconstruction with one degree of freedom per…
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, a direct finite element method is proposed for solving interface problems on unfitted meshes. This new method treats the two interface conditions as an $H^{\frac12}(\Gamma)\times H^{-\frac12}(\Gamma)$ pair for the mutual…
We develop an efficient reduced basis method for the frictional contact problem formulated using Nitsche's method. We focus on the regime of small deformations and on Tresca friction. The key idea ensuring the computational efficiency of…
We generalize the technique of [Solving Dirichlet boundary-value problems on curved domains by extensions from subdomains, SIAM J. Sci. Comput. 34, pp. A497--A519 (2012)] to elliptic problems with mixed boundary conditions and elliptic…
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…