Gradient-Finite Element Method for Nonlinear Neumann Problems

Gradient-finite Element Method for Nonlinear Neumann Problems

We consider the numerical solution of quasilinear elliptic Neumann problems. The basic difficulty is the non-injectivity of the operator, which can be overcome by suitable factorization. We extend the gradient-finite element method (GFEM), introduced earlier by the authors for Dirichlet problems, to the Neumann problem. The algorithm is constructed and its convergence is proved.

An Additive Neumann-Neumann Method for Mortar Finite Element for 4th Order Problems

In this paper, we present an additive Neumann-Neumann type parallel method for solving the system of algebraic equations arising from the mortar finite element discretization of a plate problem on a nonconforming mesh. Locally, we use a conforming Hsieh-CloughTocher macro element in the subdomains. The proposed method is almost optimal i.e. the condition number of the preconditioned problem gro...

A Finite Element Method for Nonlinear Elliptic Problems

(2013) A finite element method for nonlinear elliptic problems. This document is made available in accordance with publisher policies and may differ from the published version or from the version of record. If you wish to cite this item you are advised to consult the publisher's version. Please see the URL above for details on accessing the published version. Copyright and all moral rights to t...

An Adaptive Finite Element Method for Nonlinear Optimal Control Problems

Nitsche finite element method for parabolic problems

This paper deals with a method for the numerical solution of parabolic initialboundary value problems in two-dimensional polygonal domains Ω which are allowed to be non-convex. The Nitsche finite element method (as a mortar method) is applied for the discretization in space, i.e. non-matching meshes are used. For the discretization in time, the backward Euler method is employed. The rate of con...