Comparing numerical and exact solutions in the same 3D plot?

Questions
1

Suppose that we have:

uexact[x_, t_] := x*t;
unumeric[x_, t_] := 0.0000001 + x*t; 
Plot3D[{unumeric[x, t], uexact[x, t]}, {x, 0, 2}, {t, 0, 2}]

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  • How to create a 3d plot as follows:

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d6zw4.jpg
d6zw4.jpg640×451 62.7 KB

  • Besides, what are the best ways to comparing numerical and exact solutions in the same 3D plot? Could you share your experience?
2

This seems like a homework problem. What have you tried?

3

It’s not homework.

uexact[x_, t_] := x*t;
unumeric[x_, t_] := 0.0000001 + x*t; 
    Show[ Plot3D[ uexact[x, t], {x, 0, 2}, {t, 0, 2}], Graphics3D[{AbsolutePointSize[4], Point[ Flatten[ Table[{x, t, unumeric[x, t]}, {x, 0, 2, 0.125}, {t, 0, 2, 0.125}], 1]]}]]

I achieved it. But how to add the legends?