Caboussat, AlexandreGlowinski, RolandGourzoulidis, Dimitrios2022-09-122022-09-122022-09-122022-10-0110.1007/s10915-022-01968-8https://infoscience.epfl.ch/handle/20.500.14299/190706WOS:000844190600001We consider a least-squares/relaxation finite element method for the numerical solution of the prescribed Jacobian equation. We look for its solution via a least-squares approach. We introduce a relaxation algorithm that decouples this least-squares problem into a sequence of local nonlinear problems and variational linear problems. We develop dedicated solvers for the algebraic problems based on Newton's method and we solve the differential problems using mixed low-order finite elements. Various numerical experiments demonstrate the accuracy, efficiency and the robustness of the proposed method, compared for instance to augmented Lagrangian approaches.Mathematics, AppliedMathematicsjacobian determinantleast-squares methodnewton methodsbiharmonic regularizationfinite element methodnonlinear constrained minimizationmonge-ampere equationnumerical-solutiondirichlet problemregularitynetstext::journal::journal article::research article