Error estimates for the time discretization of an electromagnetic contact problem with moving non-magnetic conductor

2021 ◽  
Vol 87 ◽  
pp. 27-40 ◽  
Author(s):  
Van Chien Le ◽  
Marián Slodička ◽  
Karel Van Bockstal
Keyword(s):  
Contact Problem ◽  
Error Estimates ◽  
Time Discretization ◽  
Magnetic Conductor

scholarly journals A Priori and A Posteriori Error Estimates for a Crank Nicolson Type Scheme of an Elliptic Problem with Dynamical Boundary Conditions

2016 ◽  
Vol 8 (2) ◽  
pp. 1
Author(s):  
Rola Ali Ahmad ◽  
Toufic El Arwadi ◽  
Houssam Chrayteh ◽  
Jean-Marc Sac-Epee
Keyword(s):  
Error Estimates ◽  
A Priori ◽  
A Posteriori Error Estimates ◽  
Time Discretization ◽  
Posteriori Error ◽  
A Posteriori ◽  
A Posteriori Error ◽  
Dynamical Boundary Conditions ◽  
Error Indicators ◽  
Crank Nicolson

In this article we claim that we are going to give a priori and a posteriori error estimates for a Crank Nicolson type scheme. The problem is discretized by the finite elements in space. The main result of this paper consists in establishing two types of error indicators, the first one linked to the time discretization and the second one to the space discretization.

Fully discrete numerical schemes of a data assimilation algorithm: uniform-in-time error estimates

2019 ◽  
Vol 40 (4) ◽  
pp. 2584-2625 ◽  
Author(s):  
Hussain A Ibdah ◽  
Cecilia F Mondaini ◽  
Edriss S Titi
Keyword(s):  
Data Assimilation ◽  
Error Estimates ◽  
Stokes Equations ◽  
Time Discretization ◽  
Dissipative Systems ◽  
Complete Analysis ◽  
Two Dimensional ◽  
Time Error ◽  
Time Step ◽  
Fully Discrete

Abstract Our aim is to approximate a reference velocity field solving the two-dimensional Navier–Stokes equations (NSE) in the absence of its initial condition by utilizing spatially discrete measurements of that field, available at a coarse scale, and continuous in time. The approximation is obtained via numerically discretizing a downscaling data assimilation algorithm. Time discretization is based on semiimplicit and fully implicit Euler schemes, while spatial discretization (which can be done at an arbitrary scale regardless of the spatial resolution of the measurements) is based on a spectral Galerkin method. The two fully discrete algorithms are shown to be unconditionally stable, with respect to the size of the time step, the number of time steps and the number of Galerkin modes. Moreover, explicit, uniform-in-time error estimates between the approximation and the reference solution are obtained, in both the $L^2$ and $H^1$ norms. Notably, the two-dimensional NSE, subject to the no-slip Dirichlet or periodic boundary conditions, are used in this work as a paradigm. The complete analysis that is presented here can be extended to other two- and three-dimensional dissipative systems under the assumption of global existence and uniqueness.

A quasistatic frictional contact problem for viscoelastic materials with long memory

2020 ◽  
Vol 27 (2) ◽  
pp. 249-264
Author(s):  
Abderrezak Kasri ◽  
Arezki Touzaline
Keyword(s):  
Contact Problem ◽  
Coefficient Of Friction ◽  
Frictional Contact ◽  
Time Discretization ◽  
Contact Boundary ◽  
Long Term Memory ◽  
Viscoelastic Materials ◽  
Existence Of A Solution ◽  
Frictional Contact Problem ◽  
The Coefficient Of Friction

AbstractThe aim of this paper is to study a quasistatic frictional contact problem for viscoelastic materials with long-term memory. The contact boundary conditions are governed by Tresca’s law, involving a slip dependent coefficient of friction. We focus our attention on the weak solvability of the problem within the framework of variational inequalities. The existence of a solution is obtained under a smallness assumption on a normal stress prescribed on the contact surface and on the coefficient of friction. The proof is based on a time discretization method, compactness and lower semicontinuity arguments.

Error Analysis for a Galerkin Finite Element Method Applied to a Coupled Nonlinear Degenerate System of Advection-diffusion Equations

2006 ◽  
Vol 6 (1) ◽  
pp. 3-30 ◽  
Author(s):  
Koffi B. Fadimba
Keyword(s):  
Galerkin Method ◽  
Error Estimates ◽  
Time Discretization ◽  
Diffusion Equations ◽  
Degenerate System ◽  
Two Phase ◽  
Advection Diffusion ◽  
Flow Through ◽  
Standard Galerkin Method ◽  
Regularity Results

AbstractWe consider a standard Galerkin Method applied to both the pressure equation and the saturation equation of a coupled nonlinear system of degenerate advection-diffusion equations modeling a two-phase immiscible flow through porous media. After regularizing the problem and establishing some regularity results, we derive error estimates for a semi-discretized Galerkin Method. A decoupled nonlinear scheme is then proposed for a fully discretized (backward in time) Galerkin Method, and error estimates are derived for that method. We also prove the existence and uniqueness for the nonlinear operator intervening in the backward time discretization.

scholarly journals Toward error estimates for general space-time discretizations of the advection equation

2020 ◽  
Vol 23 (1-4) ◽  
Author(s):  
Martin J. Gander ◽  
Thibaut Lunet
Keyword(s):  
Error Estimates ◽  
Time Discretization ◽  
Space Time ◽  
Error Tolerance ◽  
Advection Equation ◽  
Order Of Accuracy ◽  
One Dimensional ◽  
General Space ◽  
Discretization Schemes ◽  
The One

AbstractWe develop new error estimates for the one-dimensional advection equation, considering general space-time discretization schemes based on Runge–Kutta methods and finite difference discretizations. We then derive conditions on the number of points per wavelength for a given error tolerance from these new estimates. Our analysis also shows the existence of synergistic space-time discretization methods that permit to gain one order of accuracy at a given CFL number. Our new error estimates can be used to analyze the choice of space-time discretizations considered when testing Parallel-in-Time methods.

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