We construct a family of \(C^{1}\) - \(P_{k}\) ( \(k\ge 2\) ) finite elements by enriching the \(P_k\) polynomial space with three multi-piece \(P_4\) bubble functions each triangle. The degrees of freedom on each triangle consist of the function values and the first derivatives only, no second derivatives. The global finite element space is the full \(C^1\) space while the \(C^1\) - \(P_4\) Bell element space and the \(C^1\) - \(P_k\) ( \(k\ge 5\) ) Argyris element space are proper subspaces of the \(C^1\) space on a triangular mesh. Thus the new element remains quasi-optimal for approximating piecewise smooth solutions while the other two elements fail. Numerical tests are presented, showing robustness of the new elements over the existing elements, and confirming the theory that the new elements are quasi-optimal. The new elements can be viewed as a variant of the reduced Hsieh-Clough-Tocher element when \(k=2\) , a variant of the Hsieh-Clough-Tocher element when \(k=3\) , and the Hsieh-Clough-Tocher elements with all excessive macro-bubbles removed when \(k\ge 4\) .
