Convergence and nonnegativity of numerical methods for an integrodifferential equation describing batch grinding

As a mathematical model for batch grinding we consider an integrodifferential equation of Volterra type (see (1),(2) below). Under appropriate conditions we investigate generalized solutions to this equation and semidiscretize it using a Galerkin method. We prove convergence of the semidiscretization and of the fully discretized scheme. We also investigate mass conservation and preservation of nonnegativity of the numerical solutions.