# PDE and solver settings
f = lambda x, y: 1.0
# right hand side of equation is constant
n = 3
# Order n of numerical integration
# --------------------- Loop over mesh widths --------------------------
for k in range(0, J):
# Mesh generation:
h = h_0 * 2 ** (-k / 2)
meshwidths[k] = h
print("using mesh width h = " + str(meshwidths[k]) + ":")
# define the mesh using gmsh (corners and singular points are explicitly included as nodes)
p, t, be = mesh.grid_unstr_sheet10(1.0, 0.5 * h ** 2, h, "meshes/10_4A_" + str(k))
# generate graded mesh
# node and element numbers
N = np.shape(p)[0]
M = np.shape(t)[0]
BE = np.shape(be)[0]
nodes[k] = N
elements[k] = M
print(" ", nodes[k], "nodes,", elements[k], "elements")
# -------- Identify nodes on the Dirichlet boundary ------------
insideflags = np.ones((N, 1), dtype=bool)
# will be true for all "Dirichlet-inner" points,
# i.e., points not contained in the Dirichlet boundary
energynorms = [None]*J; # ... energy norms of the discrete solutions
# PDE and solver settings
f = lambda x, y: 1.; # right hand side of equation is constant
n = 3; # Order n of numerical integration
# --------------------- Loop over mesh widths --------------------------
for k in range(0, J):
# Mesh generation:
h = h_0*2**(-k/2);
meshwidths[k] = h;
print('using mesh width h = '+str(meshwidths[k])+':');
# define the mesh using gmsh (corners and singular points are explicitly included as nodes)
p,t,be = mesh.grid_unstr_sheet10(1., h, h, 'meshes/10_3_'+str(k)); # generate quasi-uniform, unstructured mesh
# node and element numbers
N = np.shape(p)[0];
M = np.shape(t)[0];
BE = np.shape(be)[0];
nodes[k] = N;
elements[k] = M;
print(' ',nodes[k],'nodes,',elements[k],'elements')
# -------- Identify nodes on the Dirichlet boundary ------------
insideflags = np.ones((N, 1), dtype=bool); # will be true for all "Dirichlet-inner" points,
# i.e., points not contained in the Dirichlet boundary
