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

Aleksey K. Alekseev, I.M. Navon

The calculation of the temperature error at a control point as a function of approximation error of a finite difference scheme is addressed. The local truncation error is determined by 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 a guaranteed error bound may be found.