Generalized Beta Prime Distribution Applied to Finite Element Error Approximation

In this paper, we propose a new family of probability laws based on the Generalized Beta Prime distribution to evaluate relative accuracy between two Lagrange finite elements Pk1 and Pk2,(k1<k2). Usually, element is comparison asymptotic speed convergence, when mesh size h goes zero. The here highlight that there exists, depending h, cases where more likely accurate than Pk2 element. To confirm assertion, highlight, using numerical examples, quality fit statistical frequencies corresponding probabilities, as determined by law. This illustrates that, away from zero, may produce precise results Pk2, since event “Pk1is thanPk2” becomes greater 0.5. these cases, overqualified.