# A Posteriori Error Analysis via Duality TheoryPreliminaries

A Posteriori Error Analysis via Duality Theory: Preliminaries Chapter 1 1.1. INTRODUCTION Numerical simulation/scientific computation is now playing a more and more important role, and has become one of the three basic tools in science and technology, in addition to experimentation and theory. Numerical simulation provides a relatively inexpensive and efficient way to help understanding the physical world and advancing the technology. A complete numerical analysis simulation session for a physical or engineer- ing problem typically consists of several steps, described below. See Figure 1.1 for a description of the related flow chart, following . First, the physical or engineering problem is brought to our attention. We want to predict and determine the response of the physical system to the external actions. To do this we need to establish a mathematical model for the problem. This is achieved by applying physical laws, material constitutive relations, and various experimental data such as the geometry of the system, densities of external forces. Most often, we obtain an initial-boundary or boundary value problem of differential equations or differential inequalities to describe the physical or engineering problem. We call this mathematical model the basic mathematical model, and identify it with the physical reality. It is a highly idealized assumption that we http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

# A Posteriori Error Analysis via Duality TheoryPreliminaries

44 pages      /lp/springer-journals/a-posteriori-error-analysis-via-duality-theory-preliminaries-UgXQmQxkZI
Publisher
Springer US
ISBN
978-0-387-23536-3
Pages
1 –45
DOI
10.1007/0-387-23537-X_1
Publisher site
See Chapter on Publisher Site

### Abstract

Chapter 1 1.1. INTRODUCTION Numerical simulation/scientific computation is now playing a more and more important role, and has become one of the three basic tools in science and technology, in addition to experimentation and theory. Numerical simulation provides a relatively inexpensive and efficient way to help understanding the physical world and advancing the technology. A complete numerical analysis simulation session for a physical or engineer- ing problem typically consists of several steps, described below. See Figure 1.1 for a description of the related flow chart, following . First, the physical or engineering problem is brought to our attention. We want to predict and determine the response of the physical system to the external actions. To do this we need to establish a mathematical model for the problem. This is achieved by applying physical laws, material constitutive relations, and various experimental data such as the geometry of the system, densities of external forces. Most often, we obtain an initial-boundary or boundary value problem of differential equations or differential inequalities to describe the physical or engineering problem. We call this mathematical model the basic mathematical model, and identify it with the physical reality. It is a highly idealized assumption that we

Published: Jan 1, 2005

Keywords: Finite Element Method; Variational Inequality; Bilinear Form; Duality Theory; POSTERIORI Error