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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



On the coupling of boundary integral and finite element methods

Authors: Claes Johnson and J.-Claude Nédélec
Journal: Math. Comp. 35 (1980), 1063-1079
MSC: Primary 65N30
MathSciNet review: 583487
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Abstract: Let $ {\Omega ^c}$ be the complementary of a bounded regular domain in $ {{\mathbf{R}}^2}$ of boundary $ \Gamma $. We consider the problem (1)

$\displaystyle \left\{ {\begin{array}{*{20}{c}} {\Delta u = f;} & {{\text{in}}\;{\Omega ^c},} \\ {u{\vert _\Gamma } = {u_{0,}}} & {} \\ \end{array} } \right.$

where f has its support in a bounded subdomain $ {\Omega _1}$ of $ {\Omega ^c}$. Let $ {\Gamma _2}$ be the common boundary of $ {\Omega _1}$ and $ {\Omega _2} = {\Omega ^c} - {\Omega _1}$. We solve the problem (1) by using an equivalent system of equations involving an integral equation on $ {\Gamma ^2}$ coupled with the equation: (2)

$\displaystyle \left\{ {\begin{array}{*{20}{c}} {\Delta u = f} \hfill & {{\text{... ...{\vert _{{\Gamma _2}}} = \lambda .} \hfill & {} \hfill \\ \end{array} } \right.$

We introduce a finite element approximation of Eq. (2) and of the integral equation and we prove optimal error estimates.

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Article copyright: © Copyright 1980 American Mathematical Society