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- W4317464202 abstract "This paper analyzes a regularization scheme of the Monge--Amp`ere equation by uniformly elliptic Hamilton--Jacobi--Bellman equations. The main tools are stability estimates in the $L^infty$ norm from the theory of viscosity solutions which are independent of the regularization parameter $varepsilon$. They allow for the uniform convergence of the solution $u_varepsilon$ to the regularized problem towards the Alexandrov solution $u$ to the Monge--Amp`ere equation for any nonnegative $L^n$ right-hand side and continuous Dirichlet data. The main application are guaranteed a posteriori error bounds in the $L^infty$ norm for continuously differentiable finite element approximations of $u$ or $u_varepsilon$." @default.
- W4317464202 created "2023-01-20" @default.
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- W4317464202 date "2023-01-17" @default.
- W4317464202 modified "2023-10-01" @default.
- W4317464202 title "Stability and guaranteed error control of approximations to the Monge--Amp`ere equation" @default.
- W4317464202 doi "https://doi.org/10.48550/arxiv.2301.06805" @default.
- W4317464202 hasPublicationYear "2023" @default.
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