Projection-free approximation of geometrically constrained partial differential equations

We devise algorithms for the numerical approximation of partial differential equations involving a nonlinear, pointwise holonomic constraint. The elliptic, parabolic, and hyperbolic model equations are replaced by sequences of linear problems with a linear constraint. Stability and convergence hold unconditionally with respect to step sizes and triangulations. In the stationary situation a multilevel strategy is proposed that iteratively decreases the step size. Numerical experiments illustrate the accuracy of the approach.