Problem 2: A square hollow tube with side length a is split in half along the diagonal. The half consisting of the right and upper side is held at V and the lower and left side is held at -V. a) Use the finite element method used in the notebook mlaplace.nb to determine the potential inside the square. b) Plot the equipotentials within the square. c) Plot the difference between finite element potentials and the \"actual\" potentials as determined by a conformal map of the upper half plane into a square. d) Use the higher order approximation that you derived in problem 1 to get a better approximation to the potential. e) Plot the difference of the higher order approximation and the result from part (a). f) Plot the difference of the higher order approximation and the conformal map solution. Except for the corner points (which are undetermined in any approximation), how much is the greatest deviation reduced by the higher order approximation?
Added by Jordi V.
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The boundary conditions given are that the upper side is held at +V, the right side is held at +V, the lower side is held at -V, and the left side is held at -V. Show more…
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