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

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- by Zi Cai Li and Rudolf Mathon PDF
- Math. Comp.
**54**(1990), 41-61 Request permission

## 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.## References

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## Additional Information

- © Copyright 1990 American Mathematical Society
- 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