Partial Differential Equations- Scientific Computing TM

Project 2

1. Implement an adaptive solver for the heat equation based on the dG(q)-method in time and cG(1) in space.
   Allow first only adaptive time steps, and then (optional) possibly also adaptivity in space. Write your own code in Matlab for problems in one space dimension, or use readymades (via Johan Jansson) in the form of mesh generator and assembler for problems in 2 or 3 space dimensions.
2. Apply your solver to a collection of test problems
   and (optional) compute corresponding stability factors for different outputs.
3. (optional) Apply your solver to optimization/control for different pdes and goals.