Adaptive Finite Difference Methods and Implementation in the Software DUNE.

Sammanfattning

The diffusion equation is a partial differential equation that describes how quantities such as heat, particles, or other diffusive substances spread out over time and space. This type of equation can be, at often times, quite challenging to solve analytically. Finding the exact solution is often difficult due to the com- plexity of the functions involved. This thesis focuses on solving the diffusion equation using an adaptive finite difference method. We will be exploring two different methods that would produce a numerical solution. The concept of ad- aptivity optimizes our solution in a way that enhances accuracy and decreases both computational power and time. We will also be working with the DUNE software which is particularly helpful in creating adaptive grids. The software enables us to access the grid cells and it’s neighbors which will be useful when creating our solver.