Practice Example: Solving A 1d Poisson Equation Using Fem (5.3.2) - Numerical Solutions of Partial Differential Equations

Practice: Example: Solving a 1D Poisson Equation Using FEM

Lesson 5.3.2Numerical Solutions of Partial Differential Equations

Practise this section

8 questions

Flashcard drill
2 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
Sign up to start the exercise
Quiz
2 questions · about 1 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
What is the first step in applying FEM to solve a PDE?
Show hintHide hint
Think about how we break down a whole into parts.
Question 2.
Define shape functions in the context of FEM.
Show hintHide hint
These functions connect the dots!
3Question 3.
What is the main purpose of shape functions in FEM?
- To interpolate the solution
- To calculate boundaries
- To define the mesh size
Show hintHide hint
Remember, these functions are about connecting values.
4Question 4.
True or False: The weak form of a PDE is formulated to increase the derivative order.
- True
- False
Show hintHide hint
Think about why simplifying might be beneficial.
Question 5.
Given the Poisson equation with a non-linear source term, discuss how the choice of shape functions might vary.
Show hintHide hint
Think about how complexity can change our approaches.
Question 6.
Consider a domain that is not uniformly shaped. How would you adapt your finite element meshing strategy?
Show hintHide hint
Consider the terrain of the area you're working with and how it might affect element sizes.

4 more questions in this section. Enroll free to practise them all.