Conservation Properties of Iterative Methods for Implicit Discretizations of Conservation Laws

Abstract Conservation properties of iterative methods applied to implicit finite volume discretizations nonlinear conservation laws are analyzed. It is shown that any consistent multistep or Runge-Kutta method globally conservative. Further, it Newton’s method, Krylov subspace and pseudo-time iterations conservative while the Jacobi Gauss-Seidel not in general. If using an explicit a locally discretization, then resulting scheme also However, corresponding numerical flux can be inconsistent with law. We prove extension Lax-Wendroff theorem, which reveals solutions based on these converge weak modified law where function multiplied by particular constant. This constant depends choice but independent both discretization. Consistency maintained ensuring this equals unity strategy for achieving presented. Simulations show improves convergence rate iterations. Experiments GMRES suggest suffers from inconsistency automatically accounted after some number Similar experiments coarse grid corrections agglomeration indicate no inconsistency.