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This thesis focuses on the numerical analysis of partial differential equations (PDEs) with an emphasis on first and second-order fully nonlinear PDEs. The main goal is the design of numerical methods to solve a variety of equations such as orthogonal maps ...
We discuss three types of problems. The first one involves Jacobian equations and the two others involve Hessian equations. We proceed by fixed point, obtaining the results under a smallness assumption. ...
he reduced basis (RB) methods are proposed here for the solution of parametrized equations in linear elasticity problems. The fundamental idea underlying RB methods is to decouple the generation and projection stages (offline/online computational procedure ...