A Least-Squares Method for the Solution of the Non-smooth Prescribed Jacobian Equation
Alexandre Caboussat1, Roland Glowinski2,3, Dimitrios Gourzoulidis1,4
1Geneva School of Business Administration, University of Applied Sciences and Arts Western Switzerland (HES-SO), Rue de la Tambourine 17, 1227 Carouge, Geneva Switzerland.
Abstract:
We 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.
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