We obtain rates of convergence of numerical approximations of linear parabolic evolution equations. Our estimates extend known results like Theorem 3.5 in \cite{thomee} to more general equations and accommodate more advanced numerical approximation techniques. As an example, we consider parabolic equations on surfaces, and surface finite element approximations.

翻译：本文获得了线性抛物型演化方程数值逼近的收敛速率估计。我们的估计将已知结果（如\cite{thomee}中的定理3.5）推广至更一般的方程，并能适用于更先进的数值逼近技术。作为示例，我们研究了曲面上的抛物型方程及其曲面有限元逼近方法。