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math.NA2021★ 13 cited
A Carleman-based numerical method for quasilinear elliptic equations with over-determined boundary data and applications
Thuy T. Le, Loc H. Nguyen, Hung V. Tran
We propose a new iterative scheme to compute the numerical solution to an over-determined boundary value problem for a general quasilinear elliptic PDE. The main idea is to repeate…
math.NA2021★ 15 cited
Numerical viscosity solutions to Hamilton-Jacobi equations via a Carleman estimate and the convexification method
Michael Klibanov, Loc H. Nguyen, Hung V. Tran
We propose a globally convergent numerical method, called the convexification, to numerically compute the viscosity solution to first-order Hamilton-Jacobi equations through the va…