We study three mixed linear finite element methods for the numerical simulation of the two-dimensional Signorini problem. Applying Falk’s Lemma and saddle point theory to the resulting discrete mixed variational inequality allows us to state the convergence rate of each of them. Two of these finite elements provide optimal results under reasonable regularity assumptions on the Signorini solutio...

This paper presents a high-order finite element method for calculating elastic-plastic flow on moving curvilinear meshes and is an extension of our general high-order curvilinear finite element approach for solving the Euler equations of gas dynamics in a Lagrangian frame [1, 2]. In order to handle transition to plastic flow, we formulate the stress-strain relation in rate (or incremental) form...

Gradient schemes is a framework that enables the unified convergence analysis of many numerical methods for elliptic and parabolic partial differential equations: conforming and non-conforming Finite Element, Mixed Finite Element and Finite Volume methods. We show here that this framework can be applied to a family of degenerate non-linear parabolic equations (which contain in particular the Ri...

We introduce a new mixed finite element for solving the 2and 3-dimensional wave equations and equations of incompressible flow. The element, which we refer to as P1D-P2, uses discontinuous piecewise linear functions for velocity and continuous piecewise quadratic functions for pressure. The aim of introducing the mixed formulation is to produce a new flexible element choice for triangular and t...

in recent years, the application of composite materials in aircraft and space vehicle structural components has become increasingly popular. preventing failure of composite structural systems has been an important issue in engineering design. due to the lack of through-the-thickness reinforcement, structures made from laminated composite materials and adhesively bonded joints are highly suscept...

This paper presents mixed finite element methods of higher-order for a simplified Signorini problem and an idealized frictional problem. The discretization is based on a mixed variational formulation proposed by Haslinger et al. which is extended to higher-order finite elements. To guarantee the unique existence of the solution of the mixed method, a discrete inf-sup condition is proven. Approx...

We investigate a mortar technique for mixed finite element approximations of class domain decomposition saddle point problems on nonmatching grids in which the variable associated with essential boundary condition, referred to as flux, is chosen coupling variable. It plays role Lagrange multiplier impose weakly continuity natural condition. The flux-mortar incorporated use discrete extension op...