Document differences to tutorial and other useful stuff

Closes: #16 (closed)

doc/tutorial-notes.md

-# Notes on the Tutorial
-
-The [tutorial](tutorial01.pdf), and indeed the sample problem it describes was
-taken from
-[dune-pdelab-tutorials](https://gitlab.dune-project.org/pdelab/dune-pdelab-tutorials).
-PDELab is very general, and as we do not need that much generality for this
-project I made this module function without PDELab.  While this module
-replicates some functionality and concepts from PDELab, it is important to
-know what it does differently in order to understand the tutorial.  It is
-probably also helpful to give an overview over the nomenclature used in in the
-tutorial.
-
-## Nomenclature
-
-Finite Element Analysis breaks the solving a PDE down to solving a system
-
-  R(x) = 0  (R(x) is often something like Ax-b for some matrix A)
-  
-for x.  Linear solvers will typically iteratively insert better candidates x'
-for x, until they deem R(x) close enough to 0.  Thus x is called a **trial
-vector**.  On the other hand, the result of R(x) is a **test vector**, since
-that is what is tested against 0.
-
-Trial vector names: x, z, w  
-Test vector names: y, r
-
-These vectors are coefficient vectors, and together with a basis they describe
-a function mapping from the computational domain Omega into the Space of Real
-numbers.  Similar to the vectors, the functions they describe and their basis
-functions can be classified as **test function** and **trial functions** too.
-
-Trial function names: u_h (often just u)  
-Test function names: v_h (often just v)
-
-Trial space basis: { phi_i }  
-Test space basis:  { psi_j }
-
-The bases span a space of functions, the **test function space** or **trial
-function space**.
-
-Trial function space: U_h = span{ phi_i }  (sometimes just U)  
-Test function space:  V_h = span{ psi_j }  (sometimes just V)
-
-The above names apply to discrete functions and function spaces, this is made
-explicit by the subscript "_h".  Strictly speaking, the names without the
-subscript "_h" denote the undiscretized functions and function spaces, but
-these do not usually appear in code, so there the subscript is usually missing
-even though the discrete concepts are meant.
-
-The particular finite element method we use here is a Galerkin method, meaning
-that (neglecting constraints/Dirichlet boundary conditions) the function
-spaces U_h and V_h are actually identical, and are discretized by the same
-basis, i.e. phi_i = psi_i.  This can be exploited by only evaluating one basis
-and using it to compute both trial and test functions, and if this is done
-usually the trial space basis { phi_i } is used.
-
-## Differences to PDELab
-
-### Function Spaces
-
-PDELab uses the concept of grid function spaces and local function spaces.
-These have been completely removed in this module.
-
-PDELab function spaces serve multiple roles.  Local function spaces determine
-how the coefficients of multiple functions (representing multiple physical
-quantities such as pressure and velocity) are stored in the local coefficient
-vectors.  The also provide ways to evalutate the basis functions { phi_i }.
-Since the sample problem is restricted to a single physical quantity we simply
-replace the local function spaces by a local basis in the local operators, and
-store the coefficients with the same numbering in the local coefficient vector
-as the local basis uses.
-
-Grid function spaces determine where each coeffiecient is stored in the global
-vector.  As this module uses scalar P1/Q1 finite elements, it is sufficient to
-associate each coefficient with a vertex in the grid, and to use that vertices
-index (as provided by the grid view) as the coefficient's index in the global
-coefficient vector.  Grid function spaces also provide a number of other
-services, none of which are needed in our case.