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- W2783648752 abstract "This paper is concerned with continuous and discrete approximations of $W^{2,p}$ strong solutions of second-order linear elliptic partial differential equations (PDEs) in non-divergence form. The continuous approximation of these equations is achieved through the Vanishing Moment Method (VMM) which adds a small biharmonic term to the PDE. The structure of the new fourth-order PDE is a natural fit for Galerkin-type methods unlike the original second order equation since the highest order term is in divergence form. The well-posedness of the weak form of the perturbed fourth order equation is shown as well as error estimates for approximating the strong solution of the original second-order PDE. A $C^1$ finite element method is then proposed for the fourth order equation, and its existence and uniqueness of solutions as well as optimal error estimates in the $H^2$ norm are shown. Lastly, numerical tests are given to show the validity of the method." @default.
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- W2783648752 date "2018-01-17" @default.
- W2783648752 modified "2023-09-26" @default.
- W2783648752 title "Analysis of the Vanishing Moment Method and its Finite Element Approximations for Second-order Linear Elliptic PDEs in Non-divergence Form" @default.
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- W2783648752 doi "https://doi.org/10.48550/arxiv.1801.05879" @default.
- W2783648752 hasPublicationYear "2018" @default.
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