A note on space approximation of parabolic evolution equations

摘要

Our point of interest is the numerical approximation of the abstract Cauchy problemu̇(t)=Au(t),u(0)=u0∈X,where A generates an analytic semigroup in X, X being a separable Banach space. Such equations include e.g. parabolic partial differential equations of arbitrary order defined on a bounded domain. We apply semigroup methods and interpolation theory to get the order of convergence for spatially approximation in arbitrary separable Banach spaces.