MWE for moving the mesh with prescribed velocity and then remeshing selectively

remeshing_1D.py

+import dolfin as df
+
+Nx = 5
+L = 1
+
+mesh = df.IntervalMesh(Nx, 0, L)
+print(mesh.coordinates()[:, 0])
+
+def refine_mesh(mesh):
+    cell_markers = df.MeshFunction("bool", mesh, mesh.topology().dim())
+
+    for cell in df.cells(mesh):
+        if cell.h()>0.3:
+            cell_markers[cell] = True
+
+    mesh = df.refine(mesh, cell_markers)
+    return mesh
+
+for steps in range(1, 3):
+    # define a function space within the loop since mesh is changing 
+    FS = df.FunctionSpace(mesh, 'P', 1)
+
+    v = df.Function(FS)
+    v = df.project(df.Expression('x[0]*x[0]', degree=1), FS)
+
+    # move the mesh
+    dr = df.project(v * steps, FS)
+    df.ALE.move(mesh, dr)
+    
+    # refine the mesh selectively wherever a certain criteria is fulfilled
+    mesh = refine_mesh(mesh)
+    print(mesh.coordinates()[:, 0])
+
+
+