for i in range(nc):
#%% 2 Generate Mesh and FEM
n = int(5 * (2**i))
ng = 5
mesh = genMesh1D(domain, n)
fem = genFEM1D(mesh, pd)
#%% 3 Node type and DOF
fem.genBC1D(domain, bc)
#%% 4 Generate Matrices abd Vectors
Mxx = globalMatrix1D(pde.a, mesh, fem, 1, fem, 1, ng)
M0x = globalMatrix1D(pde.b, mesh, fem, 0, fem, 1, ng)
M00 = globalMatrix1D(pde.c, mesh, fem, 0, fem, 0, ng)
f = globalVec1D(pde.f, mesh, fem, 0, ng)
#%% 5 Dirichlet boundary condition
uD = pde.gD(fem.p)
uD[fem.dof] = 0.0
bxx = Mxx @ uD
b0x = M0x @ uD
b00 = M00 @ uD
#%% 6 Neumann boundary condition
bN = np.zeros(np.shape(fem.p))
bN[fem.ptype == 2] = pde.gN(fem.p[fem.ptype == 2])
#%% 7 Extract degree of freedom
ii, jj = np.meshgrid(fem.dof, fem.dof, indexing='ij')
A = Mxx[ii, jj] + M0x[ii, jj] + M00[ii, jj]
onefun = lambda x: 1.0
error_list = []
fig, axs = plt.subplots(4, 5, sharex=True, sharey=True, figsize=(20, 16))
for pd in [1, 2, 3, 4]:
file = open(f'./logs/hw2_problem2_projection_out_{pd}.log', 'w')
sys.stdout = file
for i in range(5):
n = int(4 * (2**i))
mesh = genMesh1D(domain, n)
fem = genFEM1D(mesh, pd)
M = globalMatrix1D(onefun, mesh, fem, 0, fem, 0, ng)
b = globalVec1D(fun, mesh, fem, 0, ng)
uh = inv(M) @ b
for k in range(n):
vert = mesh.p[mesh.t[k, :]]
x = np.linspace(vert[0], vert[1], 101)
uhK = uh[fem.t[k, :]]
u = evalFEfun1D(x, uhK, vert, pd, dind)
axs[pd - 1, i].plot(x, fun(x), 'k', lw=2)
axs[pd - 1, i].plot(x, u, 'r', lw=1)
axs[pd - 1, i].grid()
custom_lines = [