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SYLLABUS
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3.6 Variational inequalities
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3 FINITE ELEMENT METHOD
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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 (mid-point 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 LU-factorization and substitute Ly=b, Ux=y
perform an LU-factorization 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
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Lifelong-learners
at 07:42:53, September 25th, 2018