We develop a method to compute $H^2$-conforming finite element approximations in both two and three space dimensions using readily available finite element spaces. This is accomplished by deriving a novel, equivalent mixed variational formulation involving spaces with at most $H^1$-smoothness, so that conforming discretizations require at most $C^0$-continuity. The method is demonstrated on arbitrary order $C^1$-splines.

翻译：我们提出了一种方法，利用现成的有限元空间计算二维和三维空间中的$H^2$协调有限元逼近。这是通过推导一种新颖的、等价的混合变分形式来实现的，该形式仅涉及至多具有$H^1$光滑性的空间，因此协调离散化仅需$C^0$连续性。该方法在任意阶$C^1$样条上得到了验证。