Related papers: Augmented Lagrangian and Galerkin least squares me…
In this paper, we propose an efficient numerical treatment for solving contact problems with friction between deformable bodies. The discretized normal and tangential constraints at the candidate contact interface are expressed by using…
We propose two different Lagrange multiplier methods for contact problems derived from the augmented Lagrangian variational formulation. Both the obstacle problem, where a constraint on the solution is imposed in the bulk domain and the…
This paper addresses the problem of friction-free contact between two elastic bodies. We develop an augmented Lagrangian method that provides computational convenience by reformulating the contact problem as a nonlinear variational…
We construct a consistent multiplier free method for the finite element solution of the obstacle problem. The method is based on an augmented Lagrangian formulation in which we eliminate the multiplier by use of its definition in a discrete…
Accurate numerical simulation of coupled fracture/fault deformation and fluid flow is crucial to the performance and safety assessment of many subsurface systems. In this work, we consider the discretization and enforcement of contact…
Numerical simulations are essential for evaluating the performance and safety of geological engineered systems such as geologic carbon storage sites, enhanced geothermal fields, and oil and gas reservoirs. A key challenge lies in accurately…
In this paper we will review recent advances in the application of the augmented Lagrange multiplier method as a general approach for generating multiplier--free stabilised methods. We first show how the method generates Galerkin/Least…
In this article, we employ discontinuous Galerkin (DG) methods for the finite element approximation of the frictionless unilateral contact problem using quadratic finite elements over simplicial triangulation. We first establish an optimal…
The computational modeling of many engineering problems using the Finite Element method involves the modeling of two or more bodies that meet through an interface. The interface can be physical, as in multi-physics and contact problems, or…
The surge of activity in the resolution of fine scale features in the field of earth sciences over the past decade necessitates the development of robust yet simple algorithms that can tackle the various drawbacks of in silico models…
We use the augmented Lagrangian formalism to derive discontinuous Galerkin formulations for problems in nonlinear elasticity. In elasticity stress is typically a symmetric function of strain, leading to symmetric tangent stiffness matrices…
In this paper, we propose a linear and monolithic finite element method for the approximation of an incompressible viscous fluid interacting with an elastic and deforming plate. We use the arbitrary Lagrangian-Eulerian (ALE) approach that…
A Galerkin finite element method for the membrane elasticity problem on a meshed surface is constructed by using two-dimensional elements extended into three dimensions. The membrane finite element model is established using the intrinsic…
We construct a cut finite element method for the membrane elasticity problem on an embedded mesh using tangential differential calculus. Both free membranes and membranes coupled to 3D elasticity are considered. The discretization comes…
An arbitrary Lagrangian--Eulerian finite element method and numerical implementation for curved and deforming lipid membranes is presented here. The membrane surface is endowed with a mesh whose in-plane motion need not depend on the…
We propose a discontinuous least squares finite element method for solving the linear elasticity. The approximation space is obtained by patch reconstruction with only one unknown per element. We apply the L 2 norm least squares principle…
The purpose of this work is to study mortar methods for linear elasticity using standard low order finite element spaces. Based on residual stabilization, we introduce a stabilized mortar method for linear elasticity and compare it to the…
Mechanical contact between solids is almost exclusively modeled in Lagrangian frameworks. While these frameworks have been developed extensively and applied successfully to numerous contact problems, they generally require complex…
In a wide range of practical problems, such as forming operations and impact tests, assuming that one of the contacting bodies is rigid is an excellent approximation to the physical phenomenon. In this work, the well-established dual mortar…
In this article, we present various numerical methods to solve multi-contact problems within the Non-Smooth Discrete Element Method. The techniques considered to solve the frictional unilateral conditions are based both on the bi-potential…