Numerical Error Analysis

The use of numerical methods to approximately solve partial differential equations is widespread, yet the use of error bounds to evaluate the success of the approximation effort appears to be limited. In this section, an error bound inequality presented by Protter and Weinberger (1984) is used to generate useful information regarding the approximation of partial differential equations by numerical methods. The error bound inequality requires only boundary condition error information and approximation error information that can be readily evaluated, and the construction of an error bound function ω(x,y) as described below.