Displaying similar documents to “Numerical Analysis of a Relaxed Variational Model of Hysteresis in Two-Phase Solids”

An a posteriori error analysis for dynamic viscoelastic problems

J. R. Fernández, D. Santamarina (2011)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Similarity:

In this paper, a dynamic viscoelastic problem is numerically studied. The variational problem is written in terms of the velocity field and it leads to a parabolic linear variational equation. A fully discrete scheme is introduced by using the finite element method to approximate the spatial variable and an Euler scheme to discretize time derivatives. An error estimates result is recalled, from which the linear convergence is derived under suitable regularity conditions. Then, an error...

An error analysis for dynamic viscoelastic problems

J. R. Fernández, D. Santamarina (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

Similarity:


In this paper, a dynamic viscoelastic problem is numerically studied. The variational problem is written in terms of the velocity field and it leads to a parabolic linear variational equation. A fully discrete scheme is introduced by using the finite element method to approximate the spatial variable and an Euler scheme to discretize time derivatives. An error estimates result is recalled, from which the linear convergence is derived under suitable regularity conditions. Then, an error...

A finite element discretization of the contact between two membranes

Faker Ben Belgacem, Christine Bernardi, Adel Blouza, Martin Vohralík (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

Similarity:

From the fundamental laws of elasticity, we write a model for the contact between two membranes and we perform the analysis of the corresponding system of variational inequalities. We propose a finite element discretization of this problem and prove its well-posedness. We also establish and error estimates.

Error estimates for the ultra weak variational formulation in linear elasticity

Teemu Luostari, Tomi Huttunen, Peter Monk (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Similarity:

We prove error estimates for the ultra weak variational formulation (UWVF) in 3D linear elasticity. We show that the UWVF of Navier’s equation can be derived as an upwind discontinuous Galerkin method. Using this observation, error estimates are investigated applying techniques from the theory of discontinuous Galerkin methods. In particular, we derive a basic error estimate for the UWVF in a discontinuous Galerkin type norm and then an error estimate in the L() norm in terms of the...

Error Estimates with Post-Processing for Nonconforming Finite Elements

Friedhelm Schieweck (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Similarity:

For a nonconforming finite element approximation of an elliptic model problem, we propose error estimates in the energy norm which use as an additive term the “post-processing error” between the original nonconforming finite element solution and an easy computable conforming approximation of that solution. Thus, for the error analysis, the existing theory from the conforming case can be used together with some simple additional arguments. As an essential point, the property is...

Existence, and error estimates for a nonlinear three-field problem arising from Oldroyd-B viscoelastic flows

Marco Picasso, Jacques Rappaz (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Similarity:

In this paper, a nonlinear problem corresponding to a simplified Oldroyd-B model without convective terms is considered. Assuming the domain to be a convex polygon, existence of a solution is proved for small relaxation times. Continuous piecewise linear finite elements together with a Galerkin Least Square (GLS) method are studied for solving this problem. Existence and error estimates are established using a Newton-chord fixed point theorem, error estimates are also derived. An...