[main] Correct readme

exercises/exercise-mainfile/README.md

 # Exercise Mainfiles (DuMuX course)
-<br>
 
 ## Problem set-up
 
@@ -24,9 +23,7 @@ In the beginning, there is a uniform pressure of $1\cdot 10^5 Pa$ in the whole d
 
 * Navigate to the directory `dumux-course/exercises/exercise-mainfile`
 
-<br><br>
-### Task 1: Getting familiar with the code
-<hr>
+## Task 1: Getting familiar with the code
 
 Locate all the files you will need for this exercise
 * The __main file__ for the __incompressible, stationary__ problem : `exercise1pamain.cc`
@@ -40,8 +37,8 @@ Locate all the files you will need for this exercise
 * The __input file__ for the __compressible, instationary__ problem: `exercise_mainfile_c.input`
 
 Please pay special attention to the similarities and differences in the three main files.
-The first main file is solved linearly and does not need a newton solver or any other nonlinear solver method.
-The second problem is a nonlinear problem and uses newton's method to solve the system.
+The first main file is solved linearly and does not need a Newton solver or any other nonlinear solver method.
+The second problem is a nonlinear problem and uses Newton's method to solve the system.
 The third problem is nonlinear and additionally instationary.
 Therefore, a time loop needs to be included in the main file.
 
@@ -72,15 +69,15 @@ auto gridGeometry = std::make_shared<GridGeometry>(leafGridView);
 
 // the problem (initial and boundary conditions)
 using Problem = GetPropType<TypeTag, Properties::Problem>;
-auto problem = std::make_shared<Problem>(fvGridGeometry);
+auto problem = std::make_shared<Problem>(gridGeometry);
 
 // the solution vector
 using SolutionVector = GetPropType<TypeTag, Properties::SolutionVector>;
-SolutionVector x(fvGridGeometry->numDofs());
+SolutionVector x(gridGeometry->numDofs());
 
 // the grid variables
 using GridVariables = GetPropType<TypeTag, Properties::GridVariables>;
-auto gridVariables = std::make_shared<GridVariables>(problem, fvGridGeometry);
+auto gridVariables = std::make_shared<GridVariables>(problem, gridGeometry);
 gridVariables->init(x);
 
 // initialize the vtk output module
@@ -108,7 +105,7 @@ timeLoop->setMaxTimeStepSize(maxDt);
 
 // the assembler with time loop for instationary problem
 using Assembler = FVAssembler<TypeTag, DiffMethod::numeric>;
-auto assembler = std::make_shared<Assembler>(problem, fvGridGeometry, gridVariables, timeLoop);
+auto assembler = std::make_shared<Assembler>(problem, gridGeometry, gridVariables, timeLoop, xOld);
 
 // the linear solver
 using LinearSolver = ILUBiCGSTABIstlSolver<LinearSolverTraits<GridGeometry>, LinearAlgebraTraitsFromAssembler<Assembler>>;
@@ -149,9 +146,7 @@ timeLoop->start(); do
 timeLoop->finalize(leafGridView.comm());
 ```
 
-<br><br><br>
-### Task 2: Compiling and running an executable
-<hr>
+## Task 2: Compiling and running an executable
 
 * Change to the build-directory
 
@@ -179,9 +174,7 @@ make exercise_mainfile_a exercise_mainfile_b exercise_mainfile_c
 paraview 1p_incompressible_stationary.pvd
 ```
 
-<br><br><br>
-### Task 3: Analytical differentiation
-<hr>
+## Task 3: Analytical differentiation
 
 In the input file `exercise_mainfile_a.input`, you will see that there is a variable `BaseEpsilon`.
 This defines the base value for the epsilon used in the numeric differentiation.