Author(s) :
Robert Altmann
,
Jan Heiland
Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 052014
MSC 2000
 65J15 Equations with nonlinear operators

65M20 Method of lines

65L80 Methods for differentialalgebraic equations
Abstract :
A general framework for the regularization of constrained PDEs, also called operator DAEs, is presented.
The given procedure works for semiexplicit operator DAEs of first order which includes the NavierStokes and other flow equations.
This reformulation is a regularization in the sense that a semidiscretization 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