Hello, everyone, i am very new to FEnics. I am trying to understand the tutorial codes of Poisson equation and Heat equation. I have seen that the source function is constant in both the tutorial codes of Poisson equation and Heat equation.
Here, it is
I want to know that if my exact solutions is
uex=sin(pi*x) sin(piy) for Poisson Equation and uex(t) =exp(t) sin(pix) sin(piy) for Heat equation. Then, the source function will be non-constant and it will depends on x, y for poisson and x, y, t for Heat equation. Then, how can i write this sources in the code??. Also, how to write the exact solutions in the code so that i can compute L2 and H1 errors.
Please help. It is very needful for me.
Thanks in advance!.
Thanks sir. I got my answer for Poisson equation but i am still getting problem for Heat equation.
If uex(t)=exp(t)sin(pix)sin(piy) is the exact solution of Heat equation then how to write it code and it’s corresponding source which depends on t.
# For exact solution
import numpy as np
class exact_solution():
def __init__(self, t):
self.t = t
def __call__(self, x):
return np.exp(self.t) * np.sin(np.pi * x[0]) * np.sin(np.pi * x[1])
# For source term
import numpy as np
from dolfinx import fem
class SourceTerm:
def __init__(self):
pass # no parameters needed
def __call__(self, x, t):
return (1 + 2 * np.pi**2) * np.exp(t) * np.sin(np.pi * x[0]) * np.sin(np.pi * x[1])
from dolfinx.fem import Expression
t = 0.0 # current time
source_expr = lambda x: (1 + 2 * np.pi**2) * np.exp(t) * np.sin(np.pi * x[0]) * np.sin(np.pi * x[1])
f = fem.Expression(source_expr, X.ufl_element())
Is this above codes are fine sir for my uex(t)=exp(t)sin(pix)sin(piy) ??.
No, this is not how I would do it.
Please note that there exist a large collection of demos that cover such aspects
Most notably, you need to have a mechanism for updating t
1 Like
Okay. Thank you so much sir.
