Error and stability analysis of boundary methods for elliptic problems with interfaces

Authors:
Zi Cai Li and Rudolf Mathon

Journal:
Math. Comp. **54** (1990), 41-61

MSC:
Primary 65N10; Secondary 65N30

DOI:
https://doi.org/10.1090/S0025-5718-1990-0990600-4

MathSciNet review:
990600

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Abstract: In boundary methods, piecewise particular solutions are employed to solve a given elliptic equation within subdomains of some region of interest. A boundary approximation is then obtained by satisfying the interior and exterior boundary conditions in a least squares sense. In this paper, we examine convergence, derive error norm bounds for approximate solutions and conduct a stability analysis of the associated algebraic problem. The aim of this analysis is to help choosing good partitions of subdomains. Finally, numerical experiments are carried out for a typical interface problem, demonstrating that very accurate solutions can be obtained while at the same time keeping small the condition numbers of the associated coefficient matrices.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1990-0990600-4

Keywords:
Boundary methods,
elliptic boundary value problem,
interface,
singularity

Article copyright:
© Copyright 1990
American Mathematical Society