3.7 Computer quiz

1. Discretizing a weak form with the method of collocations, you use
   
   1. 1 evaluations of the PDE coefficients per mesh interval
   2. 2 evaluations of the PDE coefficients per mesh interval
   3. a number of evaluations depending on the order of the test function

2. Integration by part of second order differential operators
   
   1. is impossible in a cubic Galerkin FEM approximation
   2. can be used to impose natural boundary conditions
   3. is mandatory in a cubic Galerkin FEM approximation

3. With linear Galerkin FEM and constant coefficients, exact overlap integrals are
   
   1. obtained with 1 point quadratures at the cell boundary (trapezoidal rule)
   2. obtained with 1 point quadratures in the cell center (mid-point rule)
   3. obtained with 2 points Gaussian quadratures
   4. impossible to obtain with a numerical quadrature

4. Rising the implicit time parameter
   
   1. increases the numerical accuracy
   2. increases the numerical damping
   3. smoothes the physical solution
   4. none of the above

5. Rising the tunable integration parameter
   
   1. changes the numerical accuracy
   2. changes the numerical convergence
   3. smoothes the physical solution
   4. none of the above

6. For an efficient solution of a linear Galerkin FEM solution or rank you
   
   1. calculate the inverse matrix and multiply in sparse format
   2. perform an LU-factorization and substitute Ly=b, Ux=y
   3. perform an LU-factorization and substitute Uy=b, Lx=y
   4. use a direct solver in 1D, satisfied with a linear scaling in the number of operation
   5. use an iterative solver in 2D, satisfied with a cubic scaling in operations

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