曲线缩短流的稳定化BGN方法的分段线性参数有限元的超逼近与最优$L^2$收敛性
Super-approximation and optimal $L^2$ convergence of the stabilized BGN method with piecewise linear parametric finite elements for curve-shortening flow
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中文总结 AI 辅助
本文提出双同伦论证和超逼近技术，证明稳定化BGN方法在曲线缩短流中的投影误差超收敛和轨迹误差最优$L^2$收敛。
中文摘要 AI 辅助
我们发展了一种双同伦论证来估计一致性泛函的离散物质时间导数。结合分部求和，该论证在法向误差速度测试下，对一致性贡献产生方向性超收敛估计。结合反向加权离散法向的超逼近，这些技术建立了投影误差的$L_t^\infty H_x^1$超收敛性，以及用于曲线缩短流的稳定化BGN方法的分段线性参数有限元的轨迹误差的最优$L_t^\infty L_x^2$收敛性。
英文摘要
We develop a bihomotopy argument to estimate the discrete material time derivatives of consistency functionals. Combined with summation-by-parts, this argument yields a directional super-convergence estimate for the consistency contribution when tested with the normal error velocity. Together with the super-approximation of the reversely weighted discrete normal, these techniques establish $L_t^\infty H_x^1$ super-convergence of the projection error and optimal $L_t^\infty L_x^2$ convergence of the trajectory error of a stabilized BGN method for curve-shortening flow with piecewise linear parametric finite elements.
发表机构
- Old Dominion University（老道明大学）
机构由 AI 辅助整理，请以论文原文为准。
