ON THE SOLVABILITY OF THE NONLINEAR PROBLEMS IN AN ALGEBRAICALLY STABILIZED FINITE ELEMENT METHOD FOR EVOLUTIONARY TRANSPORT-DOMINATED EQUATIONS

Abstract

The so-called FEM-FCT (finite element method flux-corrected transport) scheme for evolutionary scalar convection-dominated equations leads in each time instant to a nonlinear problem. For sufficiently small time steps, the existence and uniqueness of a solution of these problems is shown.

Moreover, the convergence of a semi-smooth Newton's method is studied.

Keywords

• algebraic flux-correction
• FEM-FCT
• discrete maximum principle
• transport-dominated problems
• solvability
• uniqueness