When I refine mesh my error do not improves

mesh
1

Hello, there I am trying to perform an analysis error in fenics. I am refining my mesh intervals: 4, 8, 16, 32, and 64 intervales in the unit square. However, my error never improves. The analytical solution of my problem is 1+x^2 +2y^3.This is my code.

import numpy as np meshInteger = [4,8,16,32,64]
meshInteger = np.array(meshInteger)
errorVector = []
for i in meshInteger: from fenics import * # Create mesh and define function space
mesh = UnitSquareMesh(i, i)
V = FunctionSpace(mesh, 'Lagrange', 2) # Define boundary condition
u_D = Expression('1 + x[0]*x[0] + 2*x[1]*x[1]*x[1]', degree=3) def boundary(x, on_boundary):
return on_boundary bc = DirichletBC(V, u_D, boundary) # Define variational problem
u = TrialFunction(V)
v = TestFunction(V)
f = Expression('2+12*x[1]', degree=3)
a = dot(grad(u), grad(v))*dx
L = f*v*dx # Compute solution
u = Function(V)
solve(a == L, u, bc) # Plot solution and mesh
plot(u)
plot(mesh) # Save solution to file in VTK format
vtkfile = File('poisson/solutionPolynomial3.pvd')
vtkfile << u # Compute error in L2 norm error= errornorm(u_D, u, 'L2') # Compute maximum error at vertices
vertex_values_u_D = u_D.compute_vertex_values(mesh)
vertex_values_u = u.compute_vertex_values(mesh)
import numpy as np
error_max = np.max(np.abs(vertex_values_u_D - vertex_values_u))
errorVector.append(error) print(errorVector)#the error do not decrease

Any help and orientation of why my error is constant is highly appreciated

2

Please encapsulate your code with 3x` instead of the current formatting, as the current code cannot be copy-pasted and executed without modification.

3

And as a side-note, shouldn’t your f be multiplied by -1, as you are solving
-\nabla^2u= -\frac{\partial^2 u}{\partial^2x}-\frac{\partial^2 u}{\partial^2y}=-2-12y=f

4

Dear, Dokken. what do you mean by encapsulating with 3x?

5

Three times the backtick ` as explained at

or