# 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)
Dynamic parallel Galerkin domain decomposition procedures with grid modification for parabolic equation. (English) Zbl 1225.65096
The authors consider a diffusion-reaction parabolic equation in $d$ ($\le 3$) dimensions and continue their development of dynamic parallel Galerkin domain decomposition methods based on the work of C. N. Dawson and T. F. Dupont [Math. Comput. 58, No. 197, 21–34 (1992; Zbl 0746.65072)] and the former work by K. Ma, T. Sun and D. Yang, [Numer. Methods Partial Differ. Equations 25, No. 5, 1167–1194 (2009; Zbl 1173.65061)]. Here dynamically changing decompositions, grids in subdomains, and finite element spaces are possible, the aim being a better resolution in problems with sharp fronts and layers. They use implicit Galerkin in the subdomains and (two variants of) explicit flux calculations at inter-domain boundaries – from where a time step restriction arises. The bulk of the paper is devoted to a priori error estimates. The paper concludes with a report on numerical experiments on two-dimensional problems using bilinear elements which shows second order convergence, somewhat better ${L}_{2}$ errors than the method of Ma, Sun, and Yang [loc. cit.], but on the cost of decisively more computing time.
##### MSC:
 65M60 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (IVP of PDE) 65M55 Multigrid methods; domain decomposition (IVP of PDE) 35K57 Reaction-diffusion equations 65Y05 Parallel computation (numerical methods) 65M50 Mesh generation and refinement (IVP of PDE)