---
title: "Meaning of discretization with example"
subject: "Computational Techniques in Civil Engineering"
chapter: 1
key: "semester_8/computational_techniques_in_civil_engineering:discretization-example"
source: https://www.bctengineer.com/q/semester_8/computational_techniques_in_civil_engineering/discretization-example
site: BCT Engineering
---

# Meaning of discretization with example

Computational Techniques in Civil Engineering · Chapter 1: Introduction

- Asked in: 2075 Bhadra, 4 marks
- Video: [Lect03: Finite Element Method](https://www.youtube.com/watch?v=QyF51Q5pqQ0) — Dr. A. S. Sayyad
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_8/computational_techniques_in_civil_engineering/discretization-example
- Whole chapter: https://www.bctengineer.com/md/semester_8/computational_techniques_in_civil_engineering/chapter-1

## Question

What is meant by discretization? Describe with an example.

## Short answer

Discretisation divides a continuous domain into finite elements or grid points, reducing infinite unknowns to algebraic equations at nodes. Example: a plate with a hole is meshed with smaller elements near the hole; in FDM, a bar is divided into points to replace derivatives with difference equations.

## Answer

**Discretisation** means dividing a continuous body or domain into a finite number of smaller parts (elements, or grid points) so that a problem with infinite unknowns becomes a problem with a finite number of unknowns, usually at nodes. The continuous differential equation is then replaced by a set of algebraic equations.

**Example (FEM):** a rectangular plate with a hole under tension is divided into triangular and quadrilateral elements joined at nodes. Smaller elements are used near the hole where stress changes rapidly.

```text
 +--+--+--+--+--+
 |\ |\ |  |  |  |
 +--+--o--+--+--+     o = hole
 |  |/ |\ |  |  |
 +--+--+--+--+--+
```

Unknown displacements are found at the nodes only; displacement inside an element is obtained from shape functions.

**Example (FDM):** for a bar $u''=f(x)$ the length is divided into points $x_0,x_1,\dots,x_n$ with spacing $h$ and the equation is written at each point as
$$
\frac{u_{i-1}-2u_i+u_{i+1}}{h^2}=f_i
$$

A finer discretisation gives better accuracy but needs more computation.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What does discretisation achieve?
   A. It makes the body continuous
   B. It removes the need for equations
   C. A problem with infinite unknowns becomes one with a finite number of unknowns
   D. It makes the solution exact
   Answer: C. A continuous domain is divided into elements or grid points so differential equations become algebraic. (Key point: Meaning)

2. Why use smaller elements near a hole in a plate?
   A. Displacement is zero there
   B. Stress changes rapidly there
   C. To reduce the number of nodes
   D. Because the hole is a support
   Answer: B. Local refinement captures high stress gradients near the hole. (Key point: Mesh refinement)

3. In the FDM bar example, which equation is written at each point?
   A. (u(i-1) - 2u(i) + u(i+1))/h^2 = f(i)
   B. [K]{U} = {F} per element
   C. u = [N]{d}
   D. H u = G t
   Answer: A. The second derivative is replaced by a central difference. (Key point: FDM example)

4. What is the effect of finer discretisation?
   A. Lower accuracy and less computation
   B. No change in accuracy
   C. Better accuracy with less computation
   D. Better accuracy but more computation
   Answer: D. Finer mesh gives accuracy but costs more. (Key point: Accuracy)