zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
A reduced basis method for control problems governed by PDEs. (English) Zbl 0908.93025
Desch, W. (ed.) et al., Control and estimation of distributed parameter systems. International conference in Vorau, Austria, July 14–20, 1996. Basel: Birkhäuser. ISNM, Int. Ser. Numer. Math. 126, 153-168 (1998).
Real time simulations for optimal control of viscous flows is presented as one of the most challenging task in computational engineering and science. The difficulty is mainly due to the nonlinearity of the Navier-Stokes equations (which are the state equations for such systems), where discretizations lead to large scale control problems. The authors discuss a reduction type method called the reduced basis method in the paper. In this method, in contrast to traditional numerical methods (like finite difference or finite elements methods), where grid functions or piecewise polynomials are used as basis, one uses “very few” basis functions closely related to and generated from the problem that is being solved. The authors prove the applicability and feasibility of the reduced basis method to vorticity minimization problems in fluid flows through backward-facing step type channels. Especially attention is paid to two fluid situations. In the first one an electrically conducting fluid (as sea water for instance) under applied magnetic field and controlled by a boundary electric potential is considered. In the second situation, the control of a thermally convective fluid is effected by boundary temperature. In both cases several computational results are presented. A justification of the method is based on an error analysis.
MSC:
93B40Computational methods in systems theory
49K20Optimal control problems with PDE (optimality conditions)
49M05Numerical methods in calculus of variations based on necessary conditions
65H10Systems of nonlinear equations (numerical methods)
76W05Magnetohydrodynamics and electrohydrodynamics
80A20Heat and mass transfer, heat flow
76D05Navier-Stokes equations (fluid dynamics)