Monotonicity conditions for discretization of parabolic conservation laws, 2009

Advisors: Jan M. Nordbotten

Short description of project:

In this thesis we will extend the already existing monotonicity conditions for elliptic equations to a set of conditions for parabolic equations. These conditions is derived under the assumption that the discrete maximum principle for parabolic equations is the same as the principle for elliptic problem. Since the maximum principle for the time discrete parabolic equation is different from the principle for the elliptic equation, it may be necessary to reformulate the discrete maximum principle.  We will discuss various formulations of time discrete maximum principles together with numerical examples.

Link to thesis at BORA-UiB: Link