Targeted error indicators for use in finite-element p-adaption

A standard approach to estimating the need for new basis functions in a hierarchal finite element is to "freeze" the old degrees of freedom (i.e. the coefficients of the old basis functions) and to calculate the new degrees of freedom by applying the governing equations. Large values for the new degrees of freedom indicate that additional basis functions should be added to the element. In this work, we explore several alternatives to this, and use them as the basis for error indicators that are targeted at obtaining accuracy in a given global quantity, such as energy. These different error indicators are applied to single and multiple solution problems. The global quantities calculated are the inductance of a coil wrapped around a C-shaped core, the capacitance of a microstrip transmission line and the input impedance to two coupled coils.