# HDPG1D
This is a python package that solves 1-Dimensional PDEs using hybridizable discontinuous Petrov-Galerkin discretization, a novel FEA discretization that ensures the best solution quality without extra stablization mechanism. The following image shows the solution of 1D inviscid Burger's equation using HDPG discretization.
```math
\frac{\partial u}{\partial t} + \frac{1}{2} \frac{\partial u^2}{\partial x} = 0, \quad \text{in } \Omega \in [0,1].
```
Notice that the oscillations near the shock are well controlled even without any artificial stablization mechanism.
The main task of this project is to build an automated CFD framework based on HPDG discretization and robust adaptive mesh refinement. The solver is currently capable of solving 1D convection-diffusion equations and is being actively developed.
# Install
In the souce directory:
```bash
python setup.py sdist
cd dist/
pip install hdpg1d
```
# Usage
In terminal, call:
```bash
PGsolve
```
Follow the prompts to setup the problem, visualize the solution, and check the convergence.