<< Click to Display Table of Contents >> Navigation:  Sample Problems > Usage > Accuracy > gaus1d

{ GAUS1D.PDE

 

 This test solves a 1D heat equation with a Gaussian solution and compares

 actual deviations from the exact solution with the error estimates made by

 FlexPDE.

 The problem runs a set of ERRLIM levels and plots the history of the comparison.

 

}  

title '1D Accuracy Test - Gaussian'

 

select

   ngrid=10

   errlim = staged(1e-2, 1e-3, 1e-4, 1e-5, 1e-6)

 

coordinates

   cartesian1

 

Variables

   u

 

definitions

   k = 1

   w=0.25

   u0 = exp(-x^2/w^2)

   s = -dxx(u0)

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

 

   left=point(-1)

   right=point(1)

 

equations

   U: div(K*grad(u)) +s = 0

 

boundaries

  Region 1

      start left point value(u)=u0

      line to right point value(u)=u0

 

monitors

  elevation(u) from left to right

 

plots

  elevation(u,u0) from left to right report(errlim)

  elevation(u-u0) from left to right as "absolute error" report(errlim)

  elevation(-div(grad(u)),s) from left to right report(errlim)

 

histories

  history(RMS_error, errlim) log

 

end