Convergence Analysis for the Method of Characteristics in Unstructured Meshes
Résumé
A conservative linear surface approximation (CLS) has been recently introduced to speed up the method of characteristics in unstructured meshes. In this work, we present an analysis of the convergence of the CLS in unstructured geometries, which shows that, under optimal conditions, the method converges quadratically with the size of the regions, while the classical step characteristics approximation converges linearly. The predicted convergence rates apply only to a homogeneous convex domain with a regular boundary and regular sources and can be viewed as upper bounds for realistic heterogeneous cases. We also analyze the errors induced by the numerical implementation of the step and CLS approximations and show their impact in the final error. Numerical calculations illustrate the convergence rates.