Caboussat, AlexandreGlowinski, RolandGourzoulidis, DimitriosPicasso, Marco2020-07-312020-07-312020-07-312019-01-0110.1137/19M1243683https://infoscience.epfl.ch/handle/20.500.14299/170492WOS:000549131500023Orthogonal maps are the solutions of the mathematical model of paper-folding, also called the origami problem. They consist of a system of first-order fully nonlinear equations involving the gradient of the solution. The Dirichlet problem for orthogonal maps is considered here. A variational approach is advocated for the numerical approximation of the maps. The introduction of a suitable objective function allows us to enforce the uniqueness of the solution. A strategy based on a splitting algorithm for the corresponding flow problem is presented and leads to decoupling the time-dependent problem into a sequence of local nonlinear problems and a global linear variational problem at each time step. Numerical experiments validate the accuracy and the efficiency of the method for various domains and meshes.Mathematics, AppliedMathematicsorthogonal mapseikonal equationorigamioperator splittingfinite element methodsdynamical flowoperator splitting methodmonge-ampere equationdirichlet problemeikonal equationserror estimatorsystemtext::journal::journal article::research article