Convergence of the cell average technique for Smoluchowski coagulation equation

TL;DR

This paper analyzes the convergence of the cell average technique for solving the nonlinear Smoluchowski coagulation equation, demonstrating second order accuracy on uniform grids and first order on non-uniform grids.

Contribution

It provides a rigorous convergence analysis of the cell average technique, including its consistency and accuracy on different grid types.

Findings

Second order accuracy on uniform grids

First order accuracy on non-uniform smooth grids

Thorough discussion of the technique's consistency

Abstract

We present the convergence analysis of the cell average technique, introduced in [12], to solve the nonlinear continuous Smoluchowski coagulation equation. It is shown that the technique is second order accurate on uniform grids and first order accurate on non-uniform smooth (geometric) grids. As an essential ingredient, the consistency of the technique is thoroughly discussed.