Lec: FE2
16 important questions on Lec: FE2
How does FE work again?
With the base function, an eq has been derived to determine which fraction is assigned to each node to achieve a more continuous gradient. Compared to FV assigning more strict boundaries.
Why do we integrate the internal flux between left and right node?
Give the formula for the mean internal flux between two nodes is calculated
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Why don't we take the flux of the average state?
What is the order applied in FE 1D?
- Calculate flux everywhere
- Take average (by using the formula including an integral)
Name the two steps of the internal flux in 2D calculation
- Calculate the mean flux in the element (dark red arrow)
- Distribute this mean internal flux over the nodes of the element
- Determine amount of flow over each of the boundaries of our element/decompose of flux size for each side of the triangle, so it is perpendicular to boundaries
- Multiply with length over which it flows into/out of our element
- Assign this flux to next node
What is the difference with internal and external fluxes?
External flux just falls on your domain
What is the ironic part of FE and what is the term used to fix it?
How does Gaussian Quadrature work?
Can be used for set of eqs
gamma = weight
w = weighing factor
What are Gaussian Quadratures?
When does Gaussian Quadratures lead to errors?
But we see the eq is not linear, so obv a l inear approach will lead to errors
If dealing with highly non-linear systems, linear GQ is not the best solution. More complex versions of GQ might be better.
Which versions of GQ do you have?
Quadratic
Cubic
Quartic
What is quite ironic about the GQ calculations?
How to predict which GQ technique to use for your equation?
Even for a linear equation it might be better to use higher order GQ methods.
How is FE executed in a 2D case?
FE in 2D: we multiply with the element area rather than b-a from 1D case. And we take double integral.
Where do you solve your equation in GQ?
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