A Priori Error Estimates for Approximation of Parabolic Boundary Value Problems
Ralph E. Showalter · SIAM Journal on Numerical Analysis · 1975
The $L^2 $-error estimates are established for the continuous time Faedo–Galerkin approximation to solutions of a linear parabolic initial boundary value problem that has elliptic part of order $2m$. Properties of analytic semigroups are used to obtain these estimates directly from the $L^2 $-estimates for the corresponding steady state elliptic problem under hypotheses only on the data in the problem (initial condition, elliptic operator).