𝔖 Bobbio Scriptorium
✦   LIBER   ✦

A second-order immersed interface technique for an elliptic Neumann problem

✍ Scribed by François Bouchon; Gunther H. Peichl

Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
241 KB
Volume
23
Category
Article
ISSN
0749-159X

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

A second‐order finite difference scheme for mixed boundary value problems is presented. This scheme does not require the tangential derivative of the Neumann datum. It is designed for applications in which the Neumann condition is available only in discretized form. The second‐order convergence of the scheme is proven and the theory is validated by numerical examples. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 23: 400–420, 2007

📜 SIMILAR VOLUMES

Some New A Priori Estimates for Second-O
Some New A Priori Estimates for Second-Order Elliptic and Parabolic Interface Problems
✍ Jianguo Huang; Jun Zou 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 172 KB

We present some new a priori estimates of the solutions to the second-order elliptic and parabolic interface problems. The novelty of these estimates lies in the explicit appearance of the discontinuous coefficients and the jumps of coefficients across the interface.

An iterative procedure for solving a Cau
An iterative procedure for solving a Cauchy problem for second order elliptic equations
✍ Tomas Johansson 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 149 KB

## Abstract An iterative method for reconstruction of solutions to second order elliptic equations by Cauchy data given on a part of the boundary, is presented. At each iteration step, a series of mixed well‐posed boundary value problems are solved for the elliptic operator and its adjoint. The con

An immersed interface method for anisotr
An immersed interface method for anisotropic elliptic problems on irregular domains in 2D
✍ Miguel A. Dumett; James P. Keener 📂 Article 📅 2005 🏛 John Wiley and Sons 🌐 English ⚖ 418 KB

## Abstract This work is a generalization of the immersed interface method for discretization of a nondiagonal anisotropic Laplacian in 2D. This first‐order discretization scheme enforces weakly diagonal dominance of the numerical scheme whenever possible. A necessary and sufficient condition depen

A nonconforming mixed finite element for
A nonconforming mixed finite element for second-order elliptic problems
✍ Mohamed Farhloul; And Michel Fortin 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 131 KB 👁 2 views

In a recent work, Hiptmair [Mathematisches Institut, M9404, 1994] has constructed and analyzed a family of nonconforming mixed finite elements for second-order elliptic problems. However, his analysis does not work on the lowest order elements. In this article, we show that it is possible to constru

A Neumann–Neumann algorithm for a mortar
A Neumann–Neumann algorithm for a mortar finite element discretization of fourth-order elliptic problems in 2D
✍ Leszek Marcinkowski 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 168 KB

## Abstract Here we present and analyze a Neumann–Neumann algorithm for the mortar finite element discretization of elliptic fourth‐order problems with discontinuous coefficients. The fully parallel algorithm is analyzed using the abstract Schwarz framework, proving a convergence which is independe