Analysis of a consistency recovery method for the 1D convection–diffusion equation using linear finite elements

Published in Int. J. Numer. Meth. Fluids, Vol. 57 (9), pp. 1291-1320, 2008
Doi: 10.1002/fld.1863

Abstract

This paper introduces a new stabilized finite element method based on the finite calculus (Comput. Methods Appl. Mech. Eng. 1998; 151:233–267) and arbitrary Lagrangian–Eulerian techniques (Comput. Methods Appl. Mech. Eng. 1998; 155:235–249) for the solution to free surface problems. The main innovation of this method is the application of an overlapping domain decomposition concept in the statement of the problem. The aim is to increase the accuracy in the capture of the free surface as well as in the resolution of the governing equations in the interface between the two fluids. Free surface capturing is based on the solution to a level set equation. The Navier–Stokes equations are solved using an iterative monolithic predictor–corrector algorithm (Encyclopedia of Computational Mechanics. Wiley: New York, 2004), where the correction step is based on imposing the divergence-free condition in the velocity field by means of the solution to a scalar equation for the pressure. Examples of application of the ODDLS formulation (for overlapping domain decomposition level set) to the analysis of different free surface flow problems are presented.

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