Error estimation for solution verification of stochastic problems in PIC plasma models

When approximate methods are used to solve equations that represent a physical system of interest, a reliable and robust method of estimating the error and the convergence behavior of the model is critical to understand the quality of the solutions obtained. We present the current state of a method we´re developing to estimate error with stochastic particle-in-cell plasma models as the target model application. Richardson extrapolation is a long tried and often very useful method for investigating the error we´re interested in here. The standard application of Richardson extrapolation, however, is not adequate for our stochastic models, and so we´re extending it to suit our purpose. Foremost, a least squares method is employed to estimate the Richardson parameters from a sample of system responses. Additionally, we employ a stochastic extension of Richardson extrapolation to estimate error bounds on the parameters themselves. A Child-Langmuir diode and a sheath of ionized hydrogen are presented as quasi-steady examples of the current method.