Author(s) :
Robert Altmann
,
Jan Heiland
Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 05-2014
MSC 2000
- 65J15 Equations with nonlinear operators
-
65M20 Method of lines
-
65L80 Methods for differential-algebraic equations
Abstract :
A general framework for the regularization of constrained PDEs, also called operator DAEs, is presented.
The given procedure works for semi-explicit operator DAEs of first order which includes the Navier-Stokes and other flow equations.
This reformulation is a regularization in the sense that a semi-discretization in space leads to a DAE of lower index, i.e., of differentiation index $1$ instead of $2$.
The regularized operator DAE may help to construct numerically stable discretization schemes and thus, lead to a more efficient simulation.
Keywords :
PDAE, operator DAE, regularization, index reduction, evolution equations, method of lines, mixed finite elements