相关论文: Convergence of penalty Robin-Robin domain decompos…

In this paper we propose on continuous level several domain decomposition methods to solve unilateral and ideal multibody contact problems of nonlinear elasticity. We also present theorems about convergence of these methods.

In this paper we propose on continuous level a class of domain decomposition methods of Robin-Robin type to solve the problems of unilateral contact between elastic bodies with nonlinear Winkler covers. These methods are based on abstract…

An efficient method for solving large nonlinear problems combines Newton solvers and Domain Decomposition Methods (DDM). In the DDM framework, the boundary conditions can be chosen to be primal, dual or mixed. The mixed approach presents…

This article presents a general approach akin to domain-decomposition methods to solve a single linear PDE, but where each subdomain of a partitioned domain is associated to a distinct variational formulation coming from a mutually…

We present a convergence analysis of the penalty method applied to unilateral contact problems in two and three space dimensions. We first consider, under various regularity assumptions on the exact solution to the unilateral contact…

This paper studies the $d$-dimensional extension of a fictitious domain penalization technique that we previously proposed for Neumann or Robin boundary conditions. We apply Droniou's approach for non-coercive linear elliptic problems to…

We present Nystr\"om discretizations of multitrace formulations and non-overlapping Domain Decomposition Methods (DDM) for the solution of Helmholtz transmission problems for bounded composite scatterers with piecewise constant material…

We introduce a new overlapping Domain Decomposition Method (DDM) to solve the fully nonlinear Monge-Amp\`ere equation. While DDMs have been extensively studied for linear problems, their application to fully nonlinear partial differential…

In this work, a combined strategy of domain decomposition and the direct-line method is implemented to solve the forward and inverse linear elasticity problems of composite materials in general domains with multiple singularities. Domain…

In this work, first we employ a penalization technique to analyze a Dirichlet boundary feedback control problem pertaining to reaction-diffusion equation. We establish the stabilization result of the equivalent Robin problem in the…

In recent work, Li et al.\ (Comm.\ Math.\ Sci., 7:81-107, 2009) developed a diffuse-domain method (DDM) for solving partial differential equations in complex, dynamic geometries with Dirichlet, Neumann, and Robin boundary conditions. The…

We prove linear convergence for a new family of modified Dirichlet--Neumann methods applied to quasilinear parabolic equations, as well as the convergence of the Robin--Robin method. Such nonoverlapping domain decomposition methods are…

In this paper, we first propose and analyze a novel mixed-type DG method for the coupled Stokes-Darcy problem on simplicial meshes. The proposed formulation is locally conservative. A mixed-type DG method in conjunction with the…

This work focuses on the development and analysis of a partitioned numerical method for moving domain, fluid-structure interaction problems. We model the fluid using incompressible Navier-Stokes equations, and the structure using linear…

This paper presents a general convergence theory of penalty based numerical methods for elliptic constrained inequality problems, including variational inequalities, hemivariational inequalities, and variational-hemivariational…

Modeling contact mechanics with high contrast coefficients presents significant mathematical and computational challenges, especially in achieving strongly symmetric stress approximations for mixed formulations. Due to the inherent…

Parabolic equations on evolving domains model a multitude of applications including various industrial processes such as the molding of heated materials. Such equations are numerically challenging as they require large-scale computations…

We investigate the existence and uniqueness of (locally) absolutely continuous trajectories of a penalty term-based dynamical system associated to a constrained variational inequality expressed as a monotone inclusion problem. Relying on…

In this paper we establish the convergence of a numerical scheme based, on the Finite Element Method, for a time-independent problem modelling the deformation of a linearly elastic elliptic membrane shell subjected to remaining confined in…

A constraint penalization method is introduced within the Lattice Boltzmann (LBM) framework to model fluid-structure interactions involving rigid bodies. The proposed approach extends the fictitious domain concept by enforcing the…