Problem regarding 3D plot of a Möbius strip from a set of 2D points

Let u be the list of 2D points on a rectangle and x their transformed 3D coordinates on the Möbius strip.

{u, x} =
  Import["http://pastebin.com/raw.php?i=" <> #, "Package"] & /@
    {"x4W9hB59", "3sfTBxhV"};

Because you were doing FEM, you must also have a triangulation of the points. But you haven't provided it, so I'll assume it to be the Delaunay triangulation of u.

t = First@Cases[ListDensityPlot[Join[#, {0}] & /@ u], Polygon[idx_] :> idx, Infinity];

Render x with this triangulation:

Graphics3D[GraphicsComplex[x, {EdgeForm[], Polygon /@ t}]]

You can generate your points and the strip as follows:

pts = Table[{4 Cos[a] + r Cos[a] Cos[a/2], 
    4 Sin[a] + r Sin[a] Cos[a/2], r Sin[a/2]}, {a, 0, 2 Pi, 
    Pi/32}, {r, -2, 2, .4}];

polys = Join[#[[1]], Reverse[#[[2]]]] & /@ Partition[pts, 2, 1];

{Polygon /@ polys, Point /@ pts} // Graphics3D