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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 $ \theta\in[0.5;1]$
    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 $ p\in[0;1]$
    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 $ \mathbf{x}=\mathbf{A^{-1}b}$ or rank $ n$ 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

SYLLABUS  Previous: 3.6 Variational inequalities  Up: 3 FINITE ELEMENT METHOD  Next: 3.8 Exercises

      
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