Regularization of Constrained PDEs of Semi-Explicit Structure

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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