Pk. Moore, Interpolation error-based a posteriori error estimation for two-point boundary value problems and parabolic equations in one space dimension, NUMER MATH, 90(1), 2001, pp. 149-177
I derive a posteriori error estimates for two-point boundary value problems
and parabolic equations in one dimension based on interpolation error esti
mates. The interpolation error estimates are obtained from an extension of
the error formula for the Lagrange interpolating polynomial in the case of
symmetrically-spaced interpolation points. From this formula pointwise and
H-1 seminorm a priori estimates of the interpolation error are derived. The
interpolant in conjunction with the a priori estimates is used to obtain a
symptotically exact a posteriori error estimates of the interpolation error
. These a posteriori error estimates are extended to linear two-point bound
ary problems and parabolic equations. Computational results demonstrate the
convergence of a posteriori error estimates and their effectiveness when c
ombined with an hp-adaptive code for solving parabolic systems.