相关论文: Nitsche stabilized Virtual element approximations …

We formulate and analyze a Nitsche-type algorithm for frictional contact problems. The method is derived from, and analyzed as, a stabilized finite element method and shown to be quasi-optimal, as well as suitable as an adaptive scheme…

Wave propagation problems have many applications in physics and engineering, and the stochastic effects are important in accurately modeling them due to the uncertainty of the media. This paper considers and analyzes a fully discrete finite…

We introduce an unfitted Nitsche finite element method with a new ghost-penalty stabilization based on local projection of the solution gradient. The proposed ghost-penalty operator is straightforward to implement, ensures algebraic…

We present a hybrid mimetic finite-difference and virtual element formulation for coupled single-phase poromechanics on unstructured meshes. The key advantage of the scheme is that it is convergent on complex meshes containing highly…

The aim of this paper is to develop a virtual element method (VEM) for the vibration problem of thin plates on polygonal meshes. We consider a variational formulation relying only on the transverse displacement of the plate and propose an…

We present a multigrid method for an unfitted finite element discretization of the Dirichlet boundary value problem. The discretization employs Nitsche's method to implement the boundary condition and additional face based ghost penalties…

We establish the convergence of an adaptive spline-based finite element method of a fourth order elliptic problem with weakly-imposed Dirichlet boundary conditions using polynomial B-splines.

In this work we develop a discretisation method for the Brinkman problem that is uniformly well-behaved in all regimes (as identified by a local dimensionless number with the meaning of a friction coefficient) and supports general meshes as…

Nitsche's method is a numerical approach that weakly enforces boundary conditions for partial differential equations. In recent years, Nitsche's method has experienced a revival owing to its natural application in modern computational…

Discrete particle simulations are widely used to study large-scale particulate flows in complex geometries where particle-particle and particle-fluid interactions require an adequate representation but the computational cost has to be kept…

In this paper, a strongly mass conservative and stabilizer free scheme is designed and analyzed for the coupled Brinkman-Darcy flow and transport. The flow equations are discretized by using a strongly mass conservative scheme in mixed…

In this work, we develop and analyse a novel Hybrid High-Order discretisation of the Brinkman problem. The method hinges on hybrid discrete velocity unknowns at faces and elements and on discontinuous pressures. Based on the discrete…

Semi-discrete and fully discrete mixed finite element methods are considered for Maxwell-model-based problems of wave propagation in linear viscoelastic solid. This mixed finite element framework allows the use of a large class of existing…

We consider a mixed finite element method for a biharmonic equation with clamped boundary conditions based on biorthogonal systems with weakly imposed Dirichlet boundary condition. We show that the weak imposition of the boundary condition…

We apply the recently developed least squares stabilized symmetric Nitsche method for enforcement of Dirichlet boundary conditions to the finite cell method. The least squares stabilized Nitsche method in combination with finite cell…

The purpose of this paper is the mathematical analysis of the weak solution of the mixed Dirichlet-Robin boundary value problem for the nonlinear Darcy-Forchheimer- Brinkman system in a bounded, two-dimensional Lipschitz domain, and the…

A recent paper [J. A. Evans, D. Kamensky, Y. Bazilevs, "Variational multiscale modeling with discretely divergence-free subscales", Computers & Mathematics with Applications, 80 (2020) 2517-2537] introduced a novel stabilized finite element…

The (global) Lipschitz smoothness condition is crucial in establishing the convergence theory for most optimization methods. Unfortunately, most machine learning and signal processing problems are not Lipschitz smooth. This motivates us to…

We show the stability of a penalty-free asymmetric Nitsche's method using N\'ed\'elec edge elements for solving curl-curl-type problems with tangential Dirichlet boundary conditions imposed weakly. The main result is an inf-sup stability…

In many applications the accurate representation of the computational domain is a key factor to obtain reliable and effective numerical solutions. Curved interfaces, which might be internal, related to physical data, or portions of the…