Hierarchical B-splines
An adaptive discretization method for one-dimensional advection-diffusion problems based on hierarchical B-splines.
This was the final project for the course of Numerical Mathematics extending the results from my B.Sc. Thesis IA using Hierarchical B-Splines.
Abstract
In this work we present an adaptive discretization method for one dimensional advection-diffusion problems based on hierarchical Bsplines. After reviewing the basic theory of hierarchical B-splines and their use in FEM and similar methods, we develop algorithms for the implementation of said technique. Numerical examples are provided to test the algorithms and their MATLAB implementations.
