# 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 two-grid method for expanded mixed finite-element solution of semilinear reaction-diffusion equations. (English) Zbl 1062.65104
Summary: We present a scheme for solving two-dimensional semilinear reaction-diffusion equations using an expanded mixed finite element method. To linearize the mixed-method equations, we use a two-grid algorithm based on the Newton iteration method. The solution of a non-linear system on the fine space is reduced to the solution of two small (one linear and one non-linear) systems on the coarse space and a linear system on the fine space. It is shown that the coarse grid can be much coarser than the fine grid and achieve asymptotically optimal approximation as long as the mesh sizes satisfy $H=O\left({h}^{1/3}\right)$. As a result, solving such a large class of non-linear equation will not be much more difficult than solving one single linearized equation.
##### MSC:
 65M60 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (IVP of PDE) 35K57 Reaction-diffusion equations