We obtain rates of convergence of numerical approximations of abstract linear 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：我们获得了抽象线性演化方程数值逼近的收敛速率。本文的估计将已知结果（如\cite{thomee}中的定理3.5）推广至更一般的方程，并适用于更先进的数值逼近技术。作为示例，我们考虑了曲面上的抛物型方程及其曲面有限元逼近。