SYLLABUS Previous: 3.6 Variational inequalities
Up: 3 FINITE ELEMENT METHOD
Next: 3.8 Exercises
3.7 Computer quiz
 Discretizing a weak form with the method of collocations, you use
 1 evaluations of the PDE coefficients per mesh interval
 2 evaluations of the PDE coefficients per mesh interval
 a number of evaluations depending on the order of the test function
 Integration by part of second order differential operators
 is impossible in a cubic Galerkin FEM approximation
 can be used to impose natural boundary conditions
 is mandatory in a cubic Galerkin FEM approximation
 With linear Galerkin FEM and constant coefficients, exact overlap
integrals are
 obtained with 1 point quadratures at the cell boundary (trapezoidal rule)
 obtained with 1 point quadratures in the cell center (midpoint rule)
 obtained with 2 points Gaussian quadratures
 impossible to obtain with a numerical quadrature
 Rising the implicit time parameter
 increases the numerical accuracy
 increases the numerical damping
 smoothes the physical solution
 none of the above
 Rising the tunable integration parameter
 changes the numerical accuracy
 changes the numerical convergence
 smoothes the physical solution
 none of the above
 For an efficient solution of a linear Galerkin FEM solution
or rank
you
 calculate the inverse matrix and multiply in sparse format
 perform an LUfactorization and substitute Ly=b, Ux=y
 perform an LUfactorization and substitute Uy=b, Lx=y
 use a direct solver in 1D, satisfied with a linear scaling in the number of operation
 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
