Finite element approximation of nonlinear elliptic problems with discontinuous coefficients
Finite element approximation of nonlinear elliptic problems with discontinuous coefficients
Finite Element Approximation of the Dirichlet Problem Using the Boundary Penalty Method.
Finite element approximation of the first eigenvalue of a nonlinear problem for some special domains.
Finite Element Approximation of Viscoelastic Progressively Incompressible Flows.
Finite element approximations for the stationary large eddy simulation model
Some approximation procedures are presented for the system of equations arising from the large eddy simulation of turbulent flows. Existence of solutions to the approximate problems is proved. Discrete solutions generate a strongly convergent subsequence whose limit is a weak solution of the original problem. To prove the convergence theorem we use Young measures and related tools. We do not limit ourselves to divergence-free functions and our results are in particular valid for finite element approximations...
Finite element approximations of a glaciology problem
In this paper we study a model problem describing the movement of a glacier under Glen’s flow law and investigated by Colinge and Rappaz [Colinge and Rappaz, ESAIM: M2AN 33 (1999) 395–406]. We establish error estimates for finite element approximation using the results of Chow [Chow, SIAM J. Numer. Analysis 29 (1992) 769–780] and Liu and Barrett [Liu and Barrett, SIAM J. Numer. Analysis 33 (1996) 98–106] and give an analysis of the convergence of the successive approximations used in [Colinge and...
Finite element approximations of a glaciology problem
In this paper we study a model problem describing the movement of a glacier under Glen's flow law and investigated by Colinge and Rappaz [Colinge and Rappaz, ESAIM: M2AN33 (1999) 395–406]. We establish error estimates for finite element approximation using the results of Chow [Chow, SIAM J. Numer. Analysis29 (1992) 769–780] and Liu and Barrett [Liu and Barrett, SIAM J. Numer. Analysis33 (1996) 98–106] and give an analysis of the convergence of the successive approximations used in [Colinge and...
Finite element approximations of the three dimensional Monge-Ampère equation
In this paper, we construct and analyze finite element methods for the three dimensional Monge-Ampère equation. We derive methods using the Lagrange finite element space such that the resulting discrete linearizations are symmetric and stable. With this in hand, we then prove the well-posedness of the method, as well as derive quasi-optimal error estimates. We also present some numerical experiments that back up the theoretical findings.
Finite element approximations of the three dimensional Monge-Ampère equation
In this paper, we construct and analyze finite element methods for the three dimensional Monge-Ampère equation. We derive methods using the Lagrange finite element space such that the resulting discrete linearizations are symmetric and stable. With this in hand, we then prove the well-posedness of the method, as well as derive quasi-optimal error estimates. We also present some numerical experiments that back up the theoretical findings.
Finite element approximations of the von Kármán equations
Finite element convergence for the Darwin model to Maxwell's equations
Finite element derivative interpolation recovery technique and superconvergence
A new finite element derivative recovery technique is proposed by using the polynomial interpolation method. We show that the recovered derivatives possess superconvergence on the recovery domain and ultraconvergence at the interior mesh points for finite element approximations to elliptic boundary problems. Compared with the well-known Z-Z patch recovery technique, the advantage of our method is that it gives an explicit recovery formula and possesses the ultraconvergence for the odd-order finite...
Finite element discretization of Darcy's equations with pressure dependent porosity
We consider the flow of a viscous incompressible fluid through a rigid homogeneous porous medium. The permeability of the medium depends on the pressure, so that the model is nonlinear. We propose a finite element discretization of this problem and, in the case where the dependence on the pressure is bounded from above and below, we prove its convergence to the solution and propose an algorithm to solve the discrete system. In the case where the dependence on the pressure is exponential, we propose...
Finite element error analysis for state-constrained optimal control of the Stokes equations
Finite Element Error Estimates for Non-Linear Elliptic Equations of Monotone Type.
Finite element estimates for a class of nonlinear variational inequalities.
Finite element in modeling of flow in porous media: How to describe wells.
Finite element methods for nonlinear parabolic equations
Finite Element Methods for Nonlinear Shell Analysis.