We devise a projection-free iterative scheme for the approximation of harmonic maps that provides a second-order accuracy of the constraint violation and is unconditionally energy stable. A corresponding error estimate is valid under a mild but necessary discrete regularity condition. The method is based on the application of a BDF2 scheme and the considered problem serves as a model for partial differential equations with holonomic constraint. The performance of the method is illustrated via the computation of stationary harmonic maps and bending isometries.

翻译：我们设计了一种无投影迭代格式，用于逼近调和映射，该格式在约束违反方面具有二阶精度，且无条件能量稳定。在温和但必要的离散正则性条件下，相应的误差估计成立。该方法基于BDF2格式的应用，所考虑的问题可作为具有完整约束的偏微分方程的模型。通过计算稳态调和映射和弯曲等距，展示了该方法的性能。