poissondg.form

finite element library for mathematic majored research

# Copyright (C) 2006-2007 Kristiand Oelgaard and Anders Logg.
# Licensed under the GNU GPL version 3 or any later version.
#
# First added:  2006-12-05
# Last changed: 2007-05-09
#
# The bilinear form a(v, u) and linear form L(v) for
# Poisson's equation in a discontinuous Galerkin (DG)
# formulation.
#
# Compile this form with FFC: ffc -l dolfin Poisson.form

# Elements
DG1 = FiniteElement("Discontinuous Lagrange", "triangle", 1)
DGn = VectorElement("Discontinuous Lagrange", "triangle", 0)
DGh = FiniteElement("Discontinuous Lagrange", "triangle", 0)

# Test and trial functions
v = TestFunction(DG1)
u = TrialFunction(DG1)

# Normal component, mesh size and right-hand side
n = Function(DGn)
h = Function(DGh)
f = Function(DG1)

# Dirichlet and Neumann boundary conditions
gD = Function(DG1)
gN = Function(DG1)

# Parameters
alpha = 2.0
gamma = 100.0

# Bilinear form
#a =  dot(grad(v), grad(u))*dx \
#   - dot(avg(grad(v)), jump(u, n))*dS \
#   - dot(jump(v, n), avg(grad(u)))*dS \
#   + alpha*avg(h)*dot(jump(v, n), jump(u, n))*dS \
#   + gamma*v*u*ds

# Linear form
#L = v*f*dx + gamma*v*gD*ds + v*gN*ds

#a = dot(avg(grad(v)), jump(u, n))*dS
a = dot(avg([v, v]), jump(u, n))*dS