Enveloping algebras via motivic Hall algebras
We give a geometric realization of the whole universal enveloping algebras of Borcherds-Bozec algebras using quivers with loops via the motivic semi-derived Hall algebra approach.
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arXiv subjects
Xinyi Feng
Publications and source records attributed to Xinyi Feng.
Supercloseness of the DDG method for a singularly perturbed convection diffusion problem on Shishkin mesh
This paper investigates the supercloseness of a singularly perturbed convection diffusion problem using the direct discontinuous Galerkin (DDG) method on a Shishkin mesh. The main technical difficulties lie in controlling the diffusion term inside the layer, the convection term outside the layer, and the inter element jump term caused by the discontinuity of the numerical solution. The main idea is to design a new composite interpolation, in which a global projection is used outside the layer to satisfy the interface conditions determined by the selection of numerical flux, thereby eliminating or controlling the troublesome terms on the unit interface; and inside the layer, Gau{\ss} Lobatto projection is used to improve the convergence order of the diffusion term. On the basis of that, by selecting appropriate parameters in the numerical flux, we obtain the supercloseness result of almost $k+1$ order under an energy norm. Numerical experiments support our main theoretical conclusion.
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