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+ <use xlink:href="#DejaVuSans-Oblique-3b4" transform="translate(0 0.78125)"/>
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+ <g id="line2d_52">
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+L 231.024146 122.832281
+L 261.024146 122.832281
+" style="fill: none; stroke: #ff7f0e; stroke-width: 8; stroke-linecap: square"/>
+ </g>
+ <g id="text_14">
+ <!-- $\delta \varphi = 1.0$ -->
+ <g transform="translate(285.024146 133.332281) scale(0.3 -0.3)">
+ <use xlink:href="#DejaVuSans-Oblique-3b4" transform="translate(0 0.78125)"/>
+ <use xlink:href="#DejaVuSans-Oblique-3c6" transform="translate(61.181641 0.78125)"/>
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+ <g id="line2d_53">
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+ </g>
+ <g id="text_15">
+ <!-- $\delta \varphi = 2.0$ -->
+ <g transform="translate(551.724146 89.236969) scale(0.3 -0.3)">
+ <use xlink:href="#DejaVuSans-Oblique-3b4" transform="translate(0 0.78125)"/>
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+ </g>
+ <g id="line2d_54">
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+ </g>
+ <g id="text_16">
+ <!-- $\delta \varphi = 3.0$ -->
+ <g transform="translate(551.724146 133.332281) scale(0.3 -0.3)">
+ <defs>
+ <path id="DejaVuSans-33" d="M 2597 2516
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+ <g id="line2d_55">
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+ </g>
+ <g id="text_17">
+ <!-- $\delta \varphi = 4.0$ -->
+ <g transform="translate(818.424146 89.236969) scale(0.3 -0.3)">
+ <defs>
+ <path id="DejaVuSans-34" d="M 2419 4116
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+L 3047 0
+L 2419 0
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+ <g id="text_18">
+ <!-- $\delta \varphi = 5.0$ -->
+ <g transform="translate(818.424146 133.332281) scale(0.3 -0.3)">
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diff --git a/examples/ReproducableCode/Convergence.py b/examples/ReproducableCode/Convergence.py
index 910ed63e8f23890ea3a0a21aeca661b947538273..1dad96cac1f882bbbe8ee0c877000c7985a13695 100644
--- a/examples/ReproducableCode/Convergence.py
+++ b/examples/ReproducableCode/Convergence.py
@@ -100,3 +100,6 @@ plt.ylabel('log($L_\infty$)')
plt.grid()
plt.tight_layout()
plt.show()
+
+# Save the results
+np.savez('../Data/Convergence.npz', number_cells_vec=number_cells_vec, y_A_error_L2=y_A_error_L2, y_C_error_L2=y_C_error_L2, y_S_error_L2=y_S_error_L2, phi_error_L2=phi_error_L2, p_error_L2=p_error_L2, y_A_error_inf=y_A_error_inf, y_C_error_inf=y_C_error_inf, y_S_error_inf=y_S_error_inf, phi_error_inf=phi_error_inf, p_error_inf=p_error_inf)
\ No newline at end of file
diff --git a/examples/ReproducableCode/ShortcomingsNP.py b/examples/ReproducableCode/ShortcomingsNP.py
new file mode 100644
index 0000000000000000000000000000000000000000..8330c9c9f735dd54f9e087f7c1ac9e85f6d5fa6b
--- /dev/null
+++ b/examples/ReproducableCode/ShortcomingsNP.py
@@ -0,0 +1,123 @@
+'''
+Jan Habscheid
+Jan.Habscheid@rwth-aachen.de
+'''
+
+# import the src file needed to solve the system of equations
+import sys
+import os
+
+# Add the src directory to the sys.path
+src_path = os.path.join(os.path.dirname(os.path.abspath(__file__)), '../..', 'src')
+sys.path.insert(0, src_path)
+
+from Eq04 import solve_System_4eq
+
+# Remove the src directory from sys.path after import
+del sys.path[0]
+
+import matplotlib.pyplot as plt
+import numpy as np
+
+# Parameter and solver settings
+phi_R = 0.0
+p_R = 0.0
+y_A_R, y_C_R = 1/3, 1/3
+K = 'incompressible'
+Lambda2 = 8.553e-6
+a2 = 7.5412e-4
+number_cells = 1024
+refinement_style = 'hard_log'
+z_A, z_C = -1.0, 1.0
+relax_param = 0.05
+
+xlim = 0.025
+DeltaPhi = np.linspace(0,5,6)
+
+# Solve DGM
+y_A_Dreyer, x_Dreyer = [], []
+for phi_L in DeltaPhi:
+ y_A, y_C, phi, p, x = solve_System_4eq(phi_L, phi_R, p_R, z_A, z_C, y_A_R, y_C_R, K, Lambda2, a2, number_cells, relax_param=relax_param, return_type='Vector', refinement_style=refinement_style, max_iter=1_000)
+ y_A_Dreyer.append(y_A)
+ x_Dreyer.append(x)
+
+# Solve Nernst-Planck
+y_A_NP, x_NP = [], []
+for phi_L in DeltaPhi:
+ y_A, y_C, phi, p, x = solve_System_4eq(phi_L, phi_R, p_R, z_A, z_C, y_A_R, y_C_R, K, Lambda2, a2, number_cells, relax_param, return_type='Vector', PoissonBoltzmann=True, refinement_style=refinement_style)
+ y_A_NP.append(y_A)
+ x_NP.append(x)
+
+
+# Plotting
+labelsize = 30
+lw = 4
+legend_width = 8
+
+# fig, axs = plt.subplots(ncols=2, figsize=(30,20))
+
+# [axs[0].plot(x_NP[i], y_A_NP[i], lw=lw, label=f'$\delta \\varphi = {DeltaPhi[i]}$') for i in range(len(DeltaPhi))]
+# axs[0].set_xlim(0,xlim)
+# axs[0].set_ylim(10e-2, 1e+2)
+# axs[0].set_yscale('log')
+# axs[0].grid()
+# axs[0].set_xlabel('x [-]', fontsize=labelsize)
+# axs[0].set_ylabel('$y_A$ [-]', fontsize=labelsize)
+# axs[0].tick_params(axis='both', labelsize=labelsize)
+
+# [axs[1].plot(x_Dreyer[i], y_A_Dreyer[i], lw=lw) for i in range(len(DeltaPhi))]
+# axs[1].set_xlim(0,xlim)
+# axs[1].set_ylim(10e-2, 1e+2)
+# axs[1].set_yscale('log')
+# axs[1].grid()
+# axs[1].set_xlabel('x [-]', fontsize=labelsize)
+# axs[1].set_ylabel('$y_A$ [-]', fontsize=labelsize)
+# axs[1].tick_params(axis='both', labelsize=labelsize)
+
+# lgnd = fig.legend(bbox_to_anchor=(0.89, 1.05), fontsize=labelsize, ncol=6)
+# for line in lgnd.get_lines():
+# line.set_linewidth(legend_width)
+
+# fig.tight_layout()
+# fig.savefig('../Figures/Shortcomings_NP.svg', bbox_inches='tight')
+# fig.show()
+
+
+# Nernst-Planck
+fig, axs = plt.subplots(figsize=(15,20))
+[axs.plot(x_NP[i], y_A_NP[i], lw=lw, label=f'$\delta \\varphi = {DeltaPhi[i]}$') for i in range(len(DeltaPhi))]
+axs.set_xlim(0,xlim)
+axs.set_ylim(10e-2, 1e+2)
+axs.set_yscale('log')
+axs.grid()
+axs.set_xlabel('x [-]', fontsize=labelsize)
+axs.set_ylabel('$y_A$ [-]', fontsize=labelsize)
+axs.tick_params(axis='both', labelsize=labelsize)
+
+lgnd = fig.legend(bbox_to_anchor=(0.9, 0.97), fontsize=labelsize, ncol=3)
+for line in lgnd.get_lines():
+ line.set_linewidth(legend_width)
+
+fig.tight_layout()
+fig.savefig('../Figures/Shortcomings_NP_NP.svg', bbox_inches='tight')
+fig.show()
+
+
+# DGM
+fig, axs = plt.subplots(figsize=(15,10))
+[axs.plot(x_Dreyer[i], y_A_Dreyer[i], lw=lw, label=f'$\delta \\varphi = {DeltaPhi[i]}$') for i in range(len(DeltaPhi))]
+axs.set_xlim(0,xlim)
+axs.set_ylim(10e-2, 1.05)#1e+2)
+axs.set_yscale('log')
+axs.grid()
+axs.set_xlabel('x [-]', fontsize=labelsize)
+axs.set_ylabel('$y_A$ [-]', fontsize=labelsize)
+axs.tick_params(axis='both', labelsize=labelsize)
+
+lgnd = fig.legend(bbox_to_anchor=(0.9, 1.16), fontsize=labelsize, ncol=3)
+for line in lgnd.get_lines():
+ line.set_linewidth(legend_width)
+
+fig.tight_layout()
+fig.savefig('../Figures/Shortcomings_NP_DGM.svg', bbox_inches='tight')
+fig.show()
\ No newline at end of file
diff --git a/examples/Visualizations/VisConvergence.py b/examples/Visualizations/VisConvergence.py
new file mode 100644
index 0000000000000000000000000000000000000000..b59906d557786cf4bb1991e62fdb5b02d3f0359a
--- /dev/null
+++ b/examples/Visualizations/VisConvergence.py
@@ -0,0 +1,11 @@
+'''
+Jan Habscheid
+Jan.Habscheid@rwth-aachen.de
+'''
+
+import matplotlib.pyplot as plt
+import numpy as np
+
+
+# Load data
+data = np.load('../Data/Convergence.npz')
diff --git a/src/__pycache__/Eq04.cpython-312.pyc b/src/__pycache__/Eq04.cpython-312.pyc
index e94b79d647eeb82bdf59ecca6b780f96647b96e5..cb319838630b03ff277a650de54849d45967a0dc 100644
Binary files a/src/__pycache__/Eq04.cpython-312.pyc and b/src/__pycache__/Eq04.cpython-312.pyc differ