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{ SINE1D.PDE

 

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

 

}  

 

title '1D Accuracy test - Sine'

 

select

   ngrid=10

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

 

coordinates

   cartesian1

 

variables

   u

 

definitions

   k = 1

   h = 0.1

   w=0.1

   rs = abs(x)/w

   u0 = sin(rs)/max(rs,1e-18)

   s = -dxx(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) point value(u)=u0

      line to (1) point value(u)=u0

 

monitors

  elevation(u) from (-1) to (1)

 

plots

  elevation(u,u0) from (-1) to (1)

  elevation(u-u0) from (-1) to (1)

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

  elevation(-div(grad(u)),s) from (-1) to (1)

 

histories

  history(RMS_error,errlim) LOG

 

 

end