On the Finite Element Solution of the Pure Neumann Problem

Authors:
Pavel Bochev;R. B. Lehoucq
Affiliations:
-;-
Venue:
SIAM Review
Year:
2005

Citing 0
Cited 14

Mesh locking effects in the finite volume solution of 2-D anisotropic diffusion equations

Journal of Computational Physics
Computation of Localized Flow for Steady and Unsteady Vector Fields and Its Applications

IEEE Transactions on Visualization and Computer Graphics
On deflation and singular symmetric positive semi-definite matrices

Journal of Computational and Applied Mathematics
The immersed boundary method: A projection approach

Journal of Computational Physics
A model-based block-triangular preconditioner for the Bidomain system in electrocardiology

Journal of Computational Physics
An anisotropic mesh adaptation method for the finite element solution of variational problems

Finite Elements in Analysis and Design
Velocity-vorticity-helicity formulation and a solver for the Navier-Stokes equations

Journal of Computational Physics
A dual iterative substructuring method with a penalty term in three dimensions

Computers & Mathematics with Applications
PyDEC: Software and Algorithms for Discretization of Exterior Calculus

ACM Transactions on Mathematical Software (TOMS)
Parallel solvers for numerical upscaling

PARA'12 Proceedings of the 11th international conference on Applied Parallel and Scientific Computing
Multi-output separable Gaussian process: Towards an efficient, fully Bayesian paradigm for uncertainty quantification

Journal of Computational Physics
A nonparametric belief propagation method for uncertainty quantification with applications to flow in random porous media

Journal of Computational Physics
An isogeometric variational multiscale method for large-eddy simulation of coupled multi-ion transport in turbulent flow

Journal of Computational Physics
The DPG method for the Stokes problem

Computers & Mathematics with Applications

Quantified Score

Hi-index	0.03

Visualization

Abstract

This paper considers the finite element approximation and algebraic solution of the pure Neumann problem. Our goal is to present a concise variational framework for the finite element solution of the Neumann problem that focuses on the interplay between the algebraic and variational problems. While many of the results that stem from our analysis are known by some experts, they are seldom derived in a rigorous fashion and remain part of numerical folklore. As a result, this knowledge is not accessible (or appreciated) by many practitioners---both novices and experts---in one source. Our paper contributes a simple, yet insightful link between the continuous and algebraic variational forms that will prove useful.