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• W2546369553 abstract "We study the error estimates for the alternating evolution discontinuous Galerkin (AEDG) method to one-dimensional linear convection-diffusion equations. The AEDG method for general convection-diffusion equations was introduced by H. Liu and M. Pollack [J. Comp. Phys. 307 (2016), 574–592], where stability of the semi-discrete scheme was rigorously proved for linear problems under a CFL-like stability condition $epsilon < Qh^2$. Here $epsilon$ is the method parameter, and $h$ is the maximum spatial grid size. In this work, we establish optimal $L^2$ error estimates of order $O(h^{k+1})$ for $k$-th degree polynomials, under the same stability condition with $epsilon sim h^2$. For a fully discrete scheme with the forward Euler temporal discretization, we further obtain the $L^2$ error estimate of order $O(tau +h^{k+1})$, under the stability condition $c_0tau le epsilon < Qh^2$ for time step $tau$; and an error of order $O(tau ^2+h^{k+1})$ for the Crank-Nicolson time discretization with any time step $tau$. Key tools include two approximation spaces to distinguish overlapping polynomials, two bi-linear operators, coupled global projections, and a duality argument adapted to the situation with overlapping polynomials." @default.
• W2546369553 created "2016-11-04" @default.
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• W2546369553 date "2017-05-01" @default.
• W2546369553 modified "2023-10-16" @default.
• W2546369553 title "Error estimates for the AEDG method to one-dimensional linear convection-diffusion equations" @default.
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• W2546369553 doi "https://doi.org/10.1090/mcom/3226" @default.
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