## Abstract and Applied Analysis

- Abstr. Appl. Anal.
- Volume 2012, Special Issue (2012), Article ID 454831, 22 pages.

### FDM for Elliptic Equations with Bitsadze-Samarskii-Dirichlet Conditions

Allaberen Ashyralyev and Fatma Songul Ozesenli Tetikoglu

#### Abstract

A numerical method is proposed for solving nonlocal boundary value problem for the multidimensional elliptic partial differential equation with the Bitsadze-Samarskii-Dirichlet condition. The first and second-orders of accuracy stable difference schemes for the approximate solution of this nonlocal boundary value problem are presented. The stability estimates, coercivity, and almost coercivity inequalities for solution of these schemes are established. The theoretical statements for the solutions of these nonlocal elliptic problems are supported by results of numerical examples.

#### Article information

**Source**

Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 454831, 22 pages.

**Dates**

First available in Project Euclid: 5 April 2013

**Permanent link to this document**

https://projecteuclid.org/euclid.aaa/1365174075

**Digital Object Identifier**

doi:10.1155/2012/454831

**Mathematical Reviews number (MathSciNet)**

MR2994923

**Zentralblatt MATH identifier**

1261.65107

#### Citation

Ashyralyev, Allaberen; Ozesenli Tetikoglu, Fatma Songul. FDM for Elliptic Equations with Bitsadze-Samarskii-Dirichlet Conditions. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 454831, 22 pages. doi:10.1155/2012/454831. https://projecteuclid.org/euclid.aaa/1365174075