C++ Custom iterator class

I want to implement a custom iterator class that has some differences with typical iterators. The container in this example is a vector and the idea is to walk throw it but using a specific syntax, like this:

int main()
{

    VectorElement E;

    for (size_t i = 0; i < 5; i++)
    {
        Element e;
        e.id = i;
        E.push_back(e);
    }

    for (ElementIterator e(E); e.end(); ++e)
        cout << "Element " << e.id << endl;

}

I tried with the following definitions, but it gives me a Segmentation Fault at the static_cast line after two iterations. Does someone know how to improve this? Thanks

class Element
{
public:

    Element() {};    
    size_t id;
};

typedef vector<Element> VectorElement;

class ElementIterator: public Element
{
    typedef vector<Element>::iterator iter;

public:

    ElementIterator(const Element& e) : Element(e) { }    
    ElementIterator(VectorElement& ve_)
    {
        ve = &ve_;
        it = ve->begin();
    }

    ElementIterator operator++()
    {
        ++it;
        *this = static_cast<ElementIterator>(*it);
        return *this;
    }

    bool end()
    {
        if (it != ve->end() )
            return true;
        return false;
    }

    vector<Element>* ve;
    iter it;
};