Hi, I want to compare an exact solution of a general linear elliptic problem with DG finite element solution. I got a runtime error in my code, and do not know how to fix it.I am attaching my code here. the error massage is : " RuntimeError: In instant.recompile: The module did not compile with command 'make VERBOSE=1', see '/home/dina/.instant/error/ffc_form_d0aaf87ca6d4487091c52bef2c50a6b636a204be/compile.log' "
please help me,
my code is
# Example 1:
from dolfin import *
import numpy as np
class Linear_Elliptic_Example1(object):
'''
This is the Example_Linear_Elliptic_Example1 class
'''
def __init__(self):
self.mesh = mesh
self.boundary = DirichletBoundary()
self.boundary_value = Linear_Elliptic_Example1_solution()
self.solution = Linear_Elliptic_Example1_solution()
self.source =Linear_Elliptic_Example1_source()
return None
def __str__(self):
return 'Linear_Elliptic_Example1'
#define mesh
mesh = UnitSquareMesh(50,50, "crossed")
boundaries = FacetFunction("size_t", mesh, mesh.topology().dim()-1)
boundaries.set_all(0)
aa = Constant(100.0)
c = Constant(1.0)
# compute the exact solution and the correspunding source function
class Linear_Elliptic_Example1_solution(Expression):
def __init__(self):
return None
def eval(self, values, x):
values[0] = (1./aa)*((x[1]-x[0])*(1-x[0]-x[1])*(x[0]-0.50)**2\
*(x[1]-0.5)**2)
class Linear_Elliptic_Example1_source(Expression):
def __init__(self):
return None
def eval(self, values, x):
values[0] = (1./aa)*((x[1]-x[0])*(1-x[0]-x[1])*(x[0]-0.50)**2\
*(x[1]-0.5)**2) + 4*(1-x[0]-x[1])*(x[0]-0.5)*(x[1]-0.5)**2\
+ 4*(x[1]-x[0])*(x[0]-0.5)*(x[1]-0.5)**2-2*(x[1]-x[0])\
*(1-x[0]-x[1])*(x[1]-0.5)**2-4*(1-x[0]-x[1])*(x[0]-0.5)**2\
*(x[1]-0.5)+4*(x[1]-x[0])*(x[0]-0.5)**2*(x[1]-0.5)\
-2*(x[1]-x[0])*(1-x[0]-x[1])*(x[0]-0.5)**2
# aa* grad(u)
class Linear_Elliptic_Example1_Gradiant(Expression):
def __init__(self):
return None
def eval(self, values, x):
values[0] = -(1.-x[0]-x[1])*(x[0]-0.5)**2*(x[1]-0.5)**2-(x[1]-x[0])*(x[0]-0.5)**2\
*(x[1]-0.5)**2 + 2.*(x[1]-x[0])*(1-x[0]-x[1])*(x[0]-0.5)*(x[1]-0.5)**2
values[1] = (1.-x[0]-x[1])*(x[0]-0.5)**2*(x[1]-0.5)**2-(x[1]-x[0])*(x[0]-0.5)**2\
*(x[1]-0.5)**2 + 2.*(x[1]-x[0])*(1-x[0]-x[1])*(x[0]-0.5)**2*(x[1]-0.5)
def value_shape(self):
return (2,)
# Define function G such that G \cdot n = u_n
class BoundarySource(Expression):
def __init__(self, mesh):
self.mesh = mesh
def eval_cell(self, values, x, ufc_cell):
cell = Cell(self.mesh, ufc_cell.index)
n = cell.normal(ufc_cell.local_facet)
g = Linear_Elliptic_Example1_Gradiant()
values[0] = dot(g,n)
u_n = BoundarySource(mesh)
# Define boundary conditions
class DirichletBoundary_top(SubDomain):
def inside(self ,x, on_boundary):
return x[1] < DOLFIN_EPS
class DirichletBoundary_bottom(SubDomain):
def inside(self ,x, on_boundary):
return x[1] > 1.0 - DOLFIN_EPS
Gamma_D1 = DirichletBoundary_top()
Gamma_D1.mark(boundaries, 2)
Gamma_D2 = DirichletBoundary_top()
Gamma_D2.mark(boundaries, 4)
class NeumannBoundary_left(SubDomain):
def inside(self, x, ob_boundary):
return x[0] < DOLFIN_EPS
class NeumannBoundary_right(SubDomain):
def inside(self, x, ob_boundary):
return x[0] > 1.0 - DOLFIN_EPS
Gamma_N1 = NeumannBoundary_left()
Gamma_N1.mark(boundaries, 1)
Gamma_N2 = NeumannBoundary_right()
Gamma_N2.mark(boundaries, 3)
# Problem
V = FunctionSpace(mesh, "DG", 3)
source = Linear_Elliptic_Example1_source()
alpha = Constant(40)
h_T = CellSize(mesh)
h_T_avg = (h_T('+') + h_T('-'))/2.0
n = FacetNormal(mesh)
u = TrialFunction(V)
v = TestFunction(V)
a = dot(aa*grad(u),grad(v))*dx- dot(avg(aa*grad(u)),n)*jump(v)*dx\
+ jump(u)*dot(avg(aa*grad(v)),n)*dx\
+ alpha('+')/h_T_avg*jump(u)*jump(v)*dx
L = source*v*dx + u_n*v*ds(1) + u_n*v*ds(3)
u_top = Expression('(x[0]*(1.-x[0])*(x[0]-0.5)*(x[0]-0.5))/400.')
u_bottom = Expression('(x[0]*(x[0]-1.)*(x[0]-0.5)*(x[0]-0.5))/400.')
# Boundary conditions
bcs =[DirichletBC(V, u_top, Gamma_D1),
DirichletBC(V, u_bottom, Gamma_D2)]
# Compute solution
u_h = Function(V)
solve(a == L, u_h, bcs)
