Approximation of Elliptic PDEs and Numerical Simulation

This repository contains a collection of practical exercises for the course Approximation of elliptic PDEs and numerical simulation in the Master 1 of Applied Mathematics at Sorbonne University.

These practical works are designed to aid in understanding and applying numerical methods for approximating solutions to elliptic partial differential equations (PDEs) and simulating them computationally.

Contents

• tp1: Reminders on Python.

• tp2: Mesh management.

• tp3: Boundary and connected components.

• tp4: 1D finite elements.

• tp5: Mass and stiffness.

• tp6: Neumann/Dirichlet boundary value problem.

• project: Approximation of solutions with poor regularity.

Getting Started

To get started with these practical works, clone this repository to your local machine using:

git clone https://github.com/RyanTmi/M1-TP_EDP.git

To use this repository effectively, it is necessary to also install the pyde_fem Python package that the practical works utilize. The package is currently in the testing phase and is hosted on PyPI Test.

You can install the package using pip with the following command:

pip install -i https://test.pypi.org/simple/ pyde-fem

Make sure to install the package before proceeding with the practical works to ensure smooth execution.

Acknowledgements

Special thanks to Xavier Claeys and Émile Parolin for providing the materials and resources for this course.