Resolving entropy growth from iterative methods

Abstract We consider entropy conservative and dissipative discretizations of nonlinear conservation laws with implicit time investigate the influence iterative methods used to solve arising equations. show that Newton’s method can turn an scheme into anti-dissipative one, even when iteration error is smaller than integration error. explore several remedies, which most performant a relaxation technique, originally designed fix errors in methods. Thus, works well consort solvers, provided are on order method. To corroborate our findings, we Burgers’ equation dispersive wave find results more accurate numerical solutions non-conservative schemes, tolerance magnitude larger.