## Why does Finite Elements Methods (FEM) tile domains with triangles?

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,…

## 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… 