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)
Residual-minimization least-squares method for inverse heat conduction. (English) Zbl 0858.65098

Summary: A numerical method is systematically developed for resolving an inverse heat conduction problem in the presence of noisy discrete data. This paper illustrates the effect of imposing constraints on the unknown function of interest. A Volterra integral equation of the first kind is derived and used as the starting point for residual-minimization, least squares methodology. Symbolic manipulation is exploited for purposes of augmenting the computational methodology.

Preliminary indications suggest that the imposition of physical constraints on the system drastically reduces the level of mathematical sophistication needed for accurately approximating the unknown function of interest. These constraints are actually available in many design studies or from models which are derived by physical processes.

MSC:
65M30Improperly posed problems (IVP of PDE, numerical methods)
35K05Heat equation
65R20Integral equations (numerical methods)
45D05Volterra integral equations
35R30Inverse problems for PDE
65M60Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (IVP of PDE)