Long-time stability of finite element approximations for parabolic equations with memory
W. Allegretto, Yanping Lin, Aihui Zhou · Numerical Methods for Partial Differential Equations · 1999
In this article, we derive the sharp long-time stability and error estimates of finite element approximations for parabolic integro-differential equations. First, the exponential decay of the solution as t → ∞ is studied, and then the semidiscrete and fully discrete approximations are considered using the Ritz-Volterra projection. Other related problems are studied as well. The main feature of our analysis is that the results are valid for both smooth and nonsmooth (weakly singular) kernels. © 1999 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 15: 333–354, 1999