演化曲面上抛物型偏微分方程的后验误差估计
A posteriori error estimates for parabolic PDEs on evolving surfaces
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中文总结 AI 辅助
研究封闭演化曲面上抛物型曲面偏微分方程，推导基于残差的后验误差估计，证明误差指标有效性与可靠性，扩展自适应方法，通过数值实验说明误差渐近行为及细化粗化有效性。
中文摘要 AI 辅助
我们推导了封闭演化曲面上抛物型曲面偏微分方程基于残差的后验误差估计。主要贡献在于证明了所提出误差指标的有效性和可靠性，该指标从上方全局界定误差量，从下方在空间全局和时间局部界定误差量。我们将平稳曲面上抛物型偏微分方程的自适应方法扩展到演化曲面上允许非平凡粗化的情况。给出了多个数值实验，说明了误差的渐近行为以及细化和粗化的有效性。
英文摘要
We derive residual-based a posteriori error estimates for parabolic surface PDEs on closed evolving surfaces. The main contribution is to prove efficiency and reliability for the proposed error indicator, which bounds the error quantities globally from above and globally in space and locally in time from below. We extend methods for adaptivity for parabolic PDEs on stationary surfaces to allow for non-trivial coarsening on evolving surfaces. Multiple numerical experiments are given, which illustrate the asymptotic behaviour of the error and effectiveness of the refinement and coarsening.
