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The matched interface and boundary (MIB) method has a proven ability for delivering the second order accuracy in handling elliptic interface problems with arbitrarily complex interface geometries. However, its collocation formulation…
In this paper, we propose and analyze the least squares finite element methods for the linear elasticity interface problem in the stress-displacement system on unfitted meshes. We consider the cases that the interface is $C^2$ or polygonal,…
In this paper, we study the stability and convergence of a decoupled and linearized mixed finite element method (FEM) for incompressible miscible displacement in a porous media whose permeability and porosity are discontinuous across some…
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…
We present a new fixed mesh algorithm for solving a class of interface inverse problems for the typical elliptic interface problems. These interface inverse problems are formulated as shape optimization prob- lems whose objective…
In this paper, we introduce a class of high order immersed finite volume methods (IFVM) for one-dimensional interface problems. We show the optimal convergence of IFVM in H1 and L2 norms. We also prove some superconvergence results of IFVM.…
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…
For an elliptic problem with two space dimensions, we propose to formulate the finite volume method with the help of Petrov-Galerkin mixed finite elementsthat are based on the building of a dual Raviart-Thomas basis.
A homogenization approach is one of effective strategies to solve multiscale elliptic problems approximately. The finite element heterogeneous multiscale method (FEHMM) which is based on the finite element makes possible to simulate such…
A virtual element method (VEM) with the first order optimal convergence order is developed for solving two-dimensional Maxwell interface problems on a special class of polygonal meshes that are cut by the interface from a background…
This work introduces a novel, fully robust and highly-scalable, $h$-adaptive aggregated unfitted finite element method for large-scale interface elliptic problems. The new method is based on a recent distributed-memory implementation of the…
We consider the approximation of eigenvalue problems for elasticity equations with interface. This kind of problems can be efficiently discretized by using immersed finite element method (IFEM) based on Crouzeix-Raviart P1-nonconforming…
We propose and analyze a general framework for space-time finite element methods that is based on least-squares finite element methods for solving a first-order reformulation of the thick parabolic obstacle problem. Discretizations based on…
This paper is concerned with finite element methods for Poisson's equation with rough boundary data. Conventional methods require that the boundary data $g$ of the problem belongs to $H^{1/2} (\partial \Omega)$. However, in many…
We introduce a new class of unfitted finite element methods with high order accurate numerical integration over curved surfaces and volumes which are only implicitly defined by level set functions. An unfitted finite element method which is…
In this paper we propose a new method to stabilise non-symmetric indefinite problems. The idea is to solve a forward and an adjoint problem simultaneously using a suitable stabilised finite element method. Both stabilisation of the element…
We develop $H$(div)-conforming mixed finite element methods for the unsteady Stokes equations modeling single-phase incompressible fluid flow. A projection method in the framework of the incremental pressure correction methodology is…
We develop a cut finite element method for the Bernoulli free boundary problem. The free boundary, represented by an approximate signed distance function on a fixed background mesh, is allowed to intersect elements in an arbitrary fashion.…
This work focuses on a class of elliptic boundary value problems with diffusive, advective and reactive terms, motivated by the study of three-dimensional heterogeneous physical systems composed of two or more media separated by a selective…
A novel finite element framework is proposed for the numerical simulation of two phase flows with surface tension. The Level-Set (LS) method with piece-wise quadratic (P2) interpolation for the liquid-gas interface is used in order to reach…