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Finite element approximations of the three dimensional Monge-Ampère equation

Susanne Cecelia Brenner, Michael Neilan (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

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 derivative interpolation recovery technique and superconvergence

Tie Zhu Zhang, Shu Hua Zhang (2011)

Applications of Mathematics

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

Vivette Girault, François Murat, Abner Salgado (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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 methods on non-conforming grids by penalizing the matching constraint

Eric Boillat (2003)

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

The present paper deals with a finite element approximation of partial differential equations when the domain is decomposed into sub-domains which are meshed independently. The method we obtain is never conforming because the continuity constraints on the boundary of the sub-domains are not imposed strongly but only penalized. We derive a selection rule for the penalty parameter which ensures a quasi-optimal convergence.

Finite element methods on non-conforming grids by penalizing the matching constraint

Eric Boillat (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The present paper deals with a finite element approximation of partial differential equations when the domain is decomposed into sub-domains which are meshed independently. The method we obtain is never conforming because the continuity constraints on the boundary of the sub-domains are not imposed strongly but only penalized. We derive a selection rule for the penalty parameter which ensures a quasi-optimal convergence.

Finite element solution of a hyperbolic-parabolic problem

Rudolf Hlavička (1994)

Applications of Mathematics

Existence and finite element approximation of a hyperbolic-parabolic problem is studied. The original two-dimensional domain is approximated by a polygonal one (external approximations). The time discretization is obtained using Euler’s backward formula (Rothe’s method). Under certain smoothing assumptions on the data (see (2.6), (2.7)) the existence and uniqueness of the solution and the convergence of Rothe’s functions in the space C ( I ¯ , V ) is proved.

Finite element solution of a stationary heat conduction equation with the radiation boundary condition

Zdeněk Milka (1993)

Applications of Mathematics

In this paper we present a weak formulation of a two-dimensional stationary heat conduction problem with the radiation boundary condition. The problem can be described by an operator which is monotone on the convex set of admissible functions. The relation between classical and weak solutions as well as the convergence of the finite element method to the weak solution in the norm of the Sobolev space H 1 ( Ω ) are examined.

Currently displaying 41 – 60 of 93