Add 3D MMS collection: sinusoidal and linear Neumann & Dirichlet problems (Q1 hexahedra)

examples/Freefem/3D/mms_validation/params.json

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+{
+    "length": 1.0,
+    "youngModulus": 1e6,
+    "RatioPoisson": 0.3,
+    "nx": 5,
+    "ny": 5,
+    "nz": 5,
+    "nxConvergence": {
+        "linear_neumann":    [5, 15, 26, 36, 46, 56, 66, 76, 86],
+        "sinus_neumann":     [5, 15, 26, 36, 46, 56, 66, 76, 86],
+        "sinus_dirichlet":   [5, 15, 26, 36, 46, 56, 66, 76, 86]
+    }
+}

examples/Freefem/3D/mms_validation/sin.py

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+import numpy as np
+from utils import (
+    load_params,
+    run_simulation_3d,
+    l2_error_3d,
+    h1_error_3d,
+    plot_displacement,
+    plot_convergence,  
+    build_scene_3d,
+)
+
+CASE_NAME = "sinus_neumann"
+MODE = "sinus_neumann"
+
+
+def createScene(rootNode):
+    cfg = load_params()
+    L   = cfg["length"]
+    E   = cfg["youngModulus"]
+    nu  = cfg["RatioPoisson"]
+    nx  = cfg["nx"]
+    ny  = cfg["ny"]
+    nz  = cfg["nz"]
+    build_scene_3d(rootNode, L=L, E=E, nu=nu, nx=nx, ny=ny, nz=nz, 
+                   mode=MODE, visual=True)
+    return rootNode
+
+
+if __name__ == "__main__":
+    cfg = load_params()
+    L   = cfg["length"]
+    E   = cfg["youngModulus"]
+    nu  = cfg["RatioPoisson"]
+
+    # ========== ÉTUDE DE CONVERGENCE ==========
+    nx_list = cfg["nxConvergence"][MODE]
+
+    hs, l2s, h1s = [], [], []
+
+    for nx in nx_list:
+        ny = nz = nx
+        h = L / (nx - 1)
+
+        print(f"\n=== Maillage {nx}×{ny}×{nz} (h={h:.4f}) ===")
+
+        nodes, ux, uy, uz = run_simulation_3d(L, E, nu, nx, ny, nz, mode=MODE)
+
+        l2_err = l2_error_3d(nodes, ux, uy, uz, L, mode=MODE)
+        h1_err = h1_error_3d(nodes, ux, uy, uz, L, nx, ny, nz, mode=MODE)
+
+        hs.append(h)
+        l2s.append(l2_err)
+        h1s.append(h1_err)
+
+        if len(hs) == 1:
+            print(f"  L2 error: {l2_err:.6e}")
+            print(f"  H1 error: {h1_err:.6e}")
+        else:
+            l2_rate = np.log(l2s[-2]/l2s[-1]) / np.log(hs[-2]/hs[-1])
+            h1_rate = np.log(h1s[-2]/h1s[-1]) / np.log(hs[-2]/hs[-1])
+            print(f"  L2 error: {l2_err:.6e}  (rate {l2_rate:.2f})")
+            print(f"  H1 error: {h1_err:.6e}  (rate {h1_rate:.2f})")
+
+
+    plot_convergence(hs, l2s, h1s, mode=MODE)
+
+
+    nx = nx_list[-1]
+    ny = nz = nx
+    nodes, ux, uy, uz = run_simulation_3d(L, E, nu, nx, ny, nz, mode=MODE)
+    plot_displacement(nodes, ux, uy, uz, L, nx, ny, nz, mode=MODE)