A Study of the Modelling Error in Two Operator Splitting Algorithms for Porous Media Flow K Brusdal H K Dahle K Hvistendahl Karlsen T Mannseth

Operator splitting methods are often used to solve convection di usion prob lems of convection dominated nature However it is well known that such methods can produce signi cant splitting errors in regions containing self sharpening fronts To amend this shortcoming corrected operator splitting methods have been developed These ap proaches use the wave structure from the convection step to identify the splitting error This error is then compensated for in the di usion step The main purpose of the present work is to illustrate the importance of the correction step in the context of an inverse problem The inverse problem will consist of estimating the fractional ow function in a one dimensional saturation equation