×

zbMATH — the first resource for mathematics

A Newton iterative mixed finite element method for stationary conduction-convection problems. (English) Zbl 1267.76066
Summary: In this article, a Newton iterative mixed finite element method is presented for solving the stationary conduction-convection problems in two dimensions. The stability and the errors generated by both partitioning the space and solving nonlinear equations are analysed, which show that our method is stable and has good precision. Finally, some numerical experiments are given to confirm its effect.

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
76R10 Free convection
80A20 Heat and mass transfer, heat flow (MSC2010)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Adams R. A., Sobolev space, Pure and applied mathematics 65 (1975)
[2] DOI: 10.1080/01630569008816383 · Zbl 0714.76090
[3] Ciarlet P. G., The finite element method for elliptic problems (1978) · Zbl 0383.65058
[4] Girault V., Finite element method for Navier–Stokes equations: theory and algorithms (1987)
[5] DOI: 10.1137/S0036142901385659 · Zbl 1130.76365
[6] DOI: 10.1016/j.cma.2008.12.001 · Zbl 1227.76031
[7] DOI: 10.1007/s00607-004-0118-7 · Zbl 1099.65111
[8] DOI: 10.1137/050639910 · Zbl 1145.35318
[9] DOI: 10.1016/0096-3003(94)00134-P · Zbl 0828.76017
[10] DOI: 10.1137/0733002 · Zbl 0844.76053
[11] DOI: 10.1080/01630569408816586 · Zbl 0805.76033
[12] DOI: 10.1016/S0045-7825(01)00213-4 · Zbl 1011.76045
[13] Luo Z., Theory bases and applications of finite element mixed methods (2006)
[14] Luo Z., Mathematica Numerica Sinica 25 pp 231– (2003)
[15] Luo Z., Mathematica Numerica Sinica 25 pp 447– (2003)
[16] Luo Z., Chinese Journal of Numerical Mathematical Applications 20 pp 71– (1998)
[17] DOI: 10.1002/fld.1900 · Zbl 1161.76032
[18] DOI: 10.1016/S0096-3003(03)00591-5 · Zbl 1077.65508
[19] Reddy J. N., The finite element method transfer and fluid dynamics, 2. ed. (2000) · Zbl 0978.76003
[20] DOI: 10.1080/10618560701624518 · Zbl 1184.76868
[21] DOI: 10.1007/BF01548600
[22] DOI: 10.1080/10618560601071091 · Zbl 1110.76033
[23] DOI: 10.1007/BF02718267
[24] DOI: 10.1080/10618560412331286337 · Zbl 1286.76097
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.