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{ SPLINE_BDRY.PDE

 

 This example shows the use of the SPLINE statement in constructing boundary curves.

 

 A circular arc is approximated by five spline segments.

 The end segments are made very short to establish the proper slope at the ends.

 

 The problem solves a heatflow equation on a quarter circle and compares the solution

 with the analytic value.

 

}

title 'Spline Boundary'

Variables

   u

definitions

   k = 1

   u0 = 1-r^2

   s = 4

equations

   U: div(k*grad(u)) + s  = 0

boundaries

  Region 1

      start(0,0)

      natural(u) = 0 line to (1,0)

      value(u)=0

      spline to(0.99985,0.01745) ! short initial interval to establish slope

              to (0.866,0.5)

              to(0.5,0.866)

              to (0.01745,0.99985)   ! short final interval to establish slope

              to (0,1)

      natural(u)=0 line to close

monitors

  grid(x,y)

  contour(u)

  contour(u-u0)

plots

  grid(x,y)

  contour(u)

  contour(u-u0)

end