We obtain rates of convergence of numerical approximations of abstract linear parabolic evolution equations in Banach spaces. Our estimates extend known results from the literature of finite element approximations of parabolic equations to more general equations and numerical approximation methods. As an example, we consider parabolic equations on surfaces and surface finite element approximations.

翻译：本文获得了Banach空间中抽象线性抛物型演化方程数值逼近的收敛速率估计。我们的估计将抛物方程有限元逼近文献中的已知结果推广至更一般的方程及数值逼近方法。作为示例，我们研究了曲面上的抛物方程及曲面有限元逼近方法。