Numerical Analysis Seminar Talk, September 11, 1996

Speaker:	Professor Goong Chen, Texas A&M University
Title:	Boundary Element-Quasimonotone Iteration Scheme for Coupled 2x2 Semilinear Elliptic Partial Differential Equations
Time:	4:00pm, Wednesday, September 11, 1996
Place:	503 Blocker

Abstract:

In this talk , the speaker will discuss his recent joint work with Y.Deng, W.M. Ni and J. Zhou. Consider numerical solutions of 2x2 semilinear systems of elliptic boundary value problems, whose nonlinearities are of quasimonotone nondecreasing, quasimonotone nonincreasing, or mixed quasimonotone types. We use quasimonotone iteration; at each step, 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 2x2 matrix problem, the norm of which must be estimated. From the analysis of such 2x2 matrices, we formulate conditions which guarantee the quasimonotone 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 in our work that recently appeared in the July 1996 issue of Math. Comp. (by Deng, Chen, Ni and Zhou dealing with a single semilinear elliptic equation) for the discretized problem. Concrete examples on a 2D dumbbell-shaped domain and a 3D spherical domain featuring several types of nonlinearities are discussed and computed, and their numerical solutions are visualized by computer graphics.

Numerical Analysis Seminars

Last revised: 08/28/96 By: Tong.Sun@math.tamu.edu