Blog Posts Tagged Weak Form
How to Implement the Weak Form for Time-Dependent Equations
Here’s a comprehensive equation-based modeling guide on how to implement the weak form for time-dependent equations, including theoretical background and step-by-step instructions.
How to Implement a Point Source with the Weak Form
Today we continue our discussion on the weak formulation by looking at how to implement a point source with the weak form. A point source is a useful tool for idealizing the situation where a source is concentrated in a very small region of the modeling domain. We will find that it is very convenient to set up such a point source using the weak form.
Implementing the Weak Form with a COMSOL App
Previously in our weak form series, we discretized the weak form equation to obtain a matrix equation to solve for the unknown coefficients in our simple example problem. Following the same procedure as in this previous blog post, we will implement the equation in the COMSOL Multiphysics® software with additional steps included to examine the matrices. We will find it more convenient to use a COMSOL® software application to display all relevant matrices at once, arranged logically on one screen.
Discretizing the Weak Form Equations
This post continues our blog series on the weak formulation. In the previous post, we implemented and solved an exemplary weak form equation in the COMSOL Multiphysics software. The result was validated with simple physical arguments. Today, we will start to take a behind-the-scenes look at how the equations are discretized and solved numerically.
Implementing the Weak Form in COMSOL Multiphysics
This blog post is part of a series aimed at introducing the weak form with minimal prerequisites. In the first blog post, we learned about the basic concepts of the weak formulation. All equations were left in the analytical form. Today, we will implement and solve the equations numerically using the COMSOL Multiphysics simulation software. You are encouraged to follow the steps with a working copy of the COMSOL software.
A Brief Introduction to the Weak Form
This is an introduction to the weak form for those of us who didn’t grow up using finite element analysis and vector calculus in our daily lives, but are nevertheless interested in learning about the weak form, with the help of some physical intuition and basic calculus.