Amy,

> template <int dim>
> class BoundaryValuesU : public Function<dim>{
>    public:

You are correct: You need to tell the base class how many vector components 
your function has. You should be able to do this by adding a constructor:

   BoundaryValuesU ()
     :  Function<dim> (dim)    // your function has 'dim' components
   {}


>      virtual void vector_value(const Point<dim> & p, Vector<double> &values) 
> const override
>        {
>          double xpos, ypos, zpos;
>          xpos = p[0];
>          ypos = p[1];
>          if (dim==3){zpos=p[2];}
>          else {zpos=0.0;}
>          values[0] 
> = 
> xpos/std::pow(std::pow(xpos,2.0)+std::pow(ypos,2.0)+std::pow(zpos,2.0),0.5)*0.1;
>          values[1] 
> = 
> ypos/std::pow(std::pow(xpos,2.0)+std::pow(ypos,2.0)+std::pow(zpos,2.0),0.5)*0.1;
>          values[2] 
> = 
> zpos/std::pow(std::pow(xpos,2.0)+std::pow(ypos,2.0)+std::pow(zpos,2.0),0.5)*0.1;
>          return;
>      }

You can write this much simpler using the fact that Point objects are really 
just vectors:

   virtual void vector_value (...) const override
   {
      Tensor<1,dim> displacement = 0.1 * p / p.norm();
      for (unsigned int d=0; d<dim; ++d)
        values[d] = displacement[d];
   }

Best
  W.

-- 
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Wolfgang Bangerth          email:                 bange...@colostate.edu
                            www: http://www.math.colostate.edu/~bangerth/

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