Boundary element monotone iteration scheme for semilinear elliptic partial differential equations, Part II: Quasimonotone iteration for coupled systems
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- by Goong Chen, Yuanhua Deng, Wei-Ming Ni and Jianxin Zhou PDF
- Math. Comp. 69 (2000), 629-652 Request permission
Abstract:
Numerical solutions of $2\times 2$ semilinear systems of elliptic boundary value problems, whose nonlinearities are of quasimonotone nondecreasing, quasimonotone nonincreasing, or mixed quasimonotone types, are computed. At each step of the (quasi) monotone iteration, the solution is represented by a simple-layer potential plus a domain integral; the simple-layer density is then discretized by boundary elements. Because of the various combinations of Dirichlet, Neumann and Robin boundary conditions, there is an associated $2\times 2$ matrix problem, the norm of which must be estimated. From the analysis of such $2\times 2$ matrices, we formulate conditions which guarantee the monotone iteration a strict contraction staying within the close range of a given pair of subsolution and supersolution. Thereafter, boundary element error analysis can be carried out in a similar way as for the discretized problem. A concrete example of a monotone dissipative system on a 2D annular domain is also computed and illustrated.References
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Additional Information
- Goong Chen
- Affiliation: Department of Mathematics, Texas A&M University, College Station, TX 77843
- Email: gchen@math.tamu.edu
- Yuanhua Deng
- Affiliation: Northern Telecom, 2201 Lakeside Blvd, Richardson, Texas 75082
- Email: ydeng@nortel.ca
- Wei-Ming Ni
- Affiliation: School of Mathematics, University of Minnesota, Minneapolis, MN 55455
- MR Author ID: 130985
- Email: ni@math.umn.edu
- Jianxin Zhou
- Affiliation: Department of Mathematics, Texas A&M University, College Station, TX 77843
- Email: jzhou@math.tamu.edu
- Received by editor(s): July 15, 1996
- Received by editor(s) in revised form: April 30, 1998
- Published electronically: August 24, 1999
- Additional Notes: Professors Chen and Zhou were supported in part by NSF Grants DMS 9404380 and 9610076
Professor Ni was supported in part by NSF Grants DMS 9401333 and 9705639 - © Copyright 2000 American Mathematical Society
- Journal: Math. Comp. 69 (2000), 629-652
- MSC (1991): Primary 31B20, 35J65, 65N30
- DOI: https://doi.org/10.1090/S0025-5718-99-01109-6
- MathSciNet review: 1651745