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We devise a projection-free iterative scheme for the approximation ofharmonic maps that provides a second-order accuracy of the constraint violationand is unconditionally energy stable. A corresponding error estimate is validunder a mild but necessary discrete regularity condition. The method is basedon the application of a BDF2 scheme and the considered problem serves as amodel for partial differential equations with holonomic constraint. Theperformance of the method is illustrated via the computation of stationaryharmonic maps and bending isometries.

Quadratic constraint consistency in the projection-free approximation of harmonic maps and bending isometries