A posteriori estimates of the solution error caused by discretization in the finite element,finite difference and boundary element methods

A theory is described which guarantees an upper and lower bound estimate of the discretization error in numerical solutions of elliptic boundary value problems. This method gives bounded global estimates of the error in the energy norm. Pointwise estimates of the error in the solution variable or its derivatives can then be obtained if the numerical solution is exhibiting pointwise monotonic convergence. The versatility of this method is illustrated by its application to numerical solutions from finite element, finite difference and boundary element methods.