On a posteriori pointwise error estimation using adjoint temperature and Lagrange remainder

The pointwise estimation of heat conduction solution as a function of truncation error of a finite difference scheme is addressed. The truncation error is estimated using a Taylor series with the remainder in the Lagrange form. The contribution of the local error to the total pointwise error is estimated via an adjoint temperature. It is demonstrated that the results of numerical calculation of the temperature at an observation point may thus be refined via adjoint error correction and that an asymptotic error bound may be found.