Why is it the case that the Finite Elements Method (FEM) tiles domains with triangles? With so many geometrical shapes, is there anything special triangles have to offer? For starters,…

# Category: Numerical Analysis

## Projection methods in linear algebra numerics

Linear algebra classes often jump straight to the definition of a projector (as a matrix) when talking about orthogonal projections in linear spaces. As often as it happens, it is…

## Reproducing a transport instability in convection-diffusion equation

Drawing from Larson-Bengzon FEM book, I wanted to experiment with transport instabilities. It looks there might be an instability in my ocean-ice model but before being able to address that,…

## How do Dirichlet and Neumann boundary conditions affect Finite Element Methods variational formulations?

To solve a classical second-order differential problem with FEM, we first need to derive its weak formulation. This is achieved by multiplying the equation by a test function…

## What is the difference between Finite Differences and Finite Element Methods?

With Finite Differences, we discretize space (i.e. we put a grid on it) and we seek the values of the solution function at the mesh points. We still solve a…