Error estimates for the semidiscrete finite element approximation of linear nonlocal parabolic equations

Dennis E Jackson

doi:10.1155/s1048953392000029

Abstract

Existence and uniqueness are proved for nonlocal (in time) for solutions of linear parabolic partial differential equations. Instead of an initial condition, there is a relation connecting the initial value to values of the solution at other times. L2 error estimates are obtained for the semidiscrete approximation of the problem using finite elements in the space variables.

Highlights

Existence and uniqueness are proved for nonlocal for solutions of linear parabolic partial differential equations
We will assume for u, v (5 C([0, T]; L2(f)) of the form u, v = w, where f (t) = s(t),o(o) + s(t -)/’(, -)d, 0 we have the Lipschitz condition N
The following are some examples of g(t,..., tN, u): If hi(z) E C( ), let g(tl"’"tN’U) = hi(z)u(ti)"

Summary

Introduction

Existence and uniqueness are proved for nonlocal (in time) for solutions of linear parabolic partial differential equations. We will assume for u, v (5 C([0, T]; L2(f)) of the form u, v = w, where f (t) = s(t),o(o) + s(t -)/’(, -)d-, 0 we have the Lipschitz condition N The following are some examples of g(t,..., tN, u): If hi(z) E C( ), let g(tl"’"tN’U) = hi(z)u(ti)" Let W = C([0, T]; L2(fl)) with norm

Results

Conclusion