For the heat conduction problem, investigate the effects on the numerical solution of the following aspects:

1. non-uniform meshes with re?nement at both ends versus a uniform mesh;

2. fully implicit versus Crank-Nicolson timestepping schemes (compare accuracy and demonstrate any non-physical solution behaviour).For the contaminant transport problem, investigate the effects on the numerical solution of the following aspects:

1. fully implicit versus Crank-Nicolson timestepping schemes (compare accuracy and demonstrate any non-physical solution behaviour);

2. averaging versus upwinding advection schemes (compare accuracy and demonstrate any non-physical solution behaviour). For each investigation, you should compare the numerical solution to the exact solution and document your ?ndings in the report. You will be marked on the relevance and effectiveness of your presented results at investigating the above effects, and on your analysis of your results and how they relate to the theory covered in lectures.