Defect and adjoint error correction

Motivated by applications in aero-acoustics and electromagnetics, this paper discusses the combined use of defect correction to improve the order of accuracy of numerical solutions, and adjoint error correction to improve the order of accuracy of derived output functionals such as far-field boundary integrals. Numerical results for the 1D Helmholtz equation on an irregular grid show fourth order accuracy for the numerical solution, and sixth order accuracy for the boundary value.