Abstract

Conventional accuracy analysis of finite element methods depends on the Schwarz inequality which yields the optimal accuracy for general meshes. However, for constructed meshes higher order of accuracy may be obtained without using the Schwarz inequality. Instead, we should use the “identity method” to recover the full accuracy. Especially for convection-diffusion problems involving small parameters, the traditional estimate certainly depends on the parameters and thus we can not obtain the optimal result. By using the “identity method” together with the properties of the target problems, we can obtain the optimal accuracy independent of the parameters. Moreover, the “identity method” only uses the integration by parts, thus most math postgraduate students may follow the approaches used.