Mon Nov 17 11:29:32 2014

FEM1D_HEAT_EXPLICIT_TEST
  Python version.
  Test the FEM1D_HEAT_EXPLICIT library.

FEM1D_HEAT_EXPLICIT_TEST01:
  The time dependent 1D heat equation is

    Ut - k * Uxx = f(x,t)

  for space interval A <= X <= B with boundary conditions

    U(A,t) = UA(t)
    U(B,t) = UB(t)

  and time interval T0 <= T <= T1 with initial condition

    U(X,T0) = U0(X).

  To compute an approximate solution:
    the interval [A,B] is replace by a discretized mesh Xi
    a set of finite element functions PSI(X) are determined,
    the solution U is written as a weighted sum of the basis functions,
    the weak form of the differential equation is written,
    a time grid Tj is imposed, and time derivatives replaced by
    an explicit forward Euler first difference,

    The continuous PDE has now been transformed into a set of algebraic
    equations for the coefficients C(Xi,Tj).

  Number of X nodes = 21
  X interval = [ 0.000000, 1.000000 ]
  X step size = 0.050000
  Number of T steps = 401
  T interval = [ 0.000000, 80.000000 ]
  T step size = 0.200000
  Number of elements = 20
  Number of quadrature points = 3