Boundary element monotone iteration scheme for semilinear elliptic partial differential equations, part II: quasimonotone iteration for coupled 2 × 2 systems

Goong Chen, Yuanhua Deng, Wei Ming Ni, Jianxin Zhou

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2 Scopus citations

Abstract

Numerical solutions of 2 × 2 sernilinear 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 × 2 matrix problem, the norm of which must be estimated. Prom the analysis of such 2 × 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.

Original languageEnglish (US)
Pages (from-to)629-652
Number of pages24
JournalMathematics of Computation
Volume69
Issue number230
DOIs
StatePublished - Apr 2000

Keywords

  • Boundary elements
  • Error analysis
  • Lotka-Volterra models
  • Nonlinear elliptic systems

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