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{ SINE2D.PDE

 

 This problem compares the solution accuracy for four different levels of ERRLIM.  

 

}  

 

title '2D Accuracy Test - Sine'

 

select

   ngrid = 5

   errlim = staged(1e-2, 1e-3, 1e-4, 1e-5)

 

variables

   u

 

definitions

   k = 1

   h = 0.1

   w=0.1

   rs = r/w

   u0 = sin(rs)/rs

   s = -dxx(u0)-dyy(u0)

   RMS_error = sqrt(integral((u-u0)^2)/sqrt(integral(u0^2)))

 

equations

   U: div(K*grad(u)) +s = 0

 

boundaries

  Region 1

      start(-1,-1) value(u)=u0

      line to (1,-1) to (1,1) to (-1,1) to close

 

monitors

  grid(x,y)

  contour(u)

 

plots

  grid(x,y)

  contour(u)

  elevation(u,u0) from(-1,0) to (1,0)

  elevation(u-u0) from(-1,0) to (1,0)

  elevation(dx(u),dx(u0)) from(-1,0) to (1,0)

  elevation(dxx(u),dxx(u0)) from(-1,0) to (1,0)

  elevation(dxx(u)+dyy(u),-s) from(-1,0) to (1,0)

  contour(dxx(u)) contour(dxy(u)) contour(dyy(u))

 

histories

  history(RMS_error, errlim) LOG

 

end