# Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

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## On the coupling of boundary integral and finite element methodsHTML articles powered by AMS MathViewer

by Claes Johnson and J.-Claude Nédélec
Math. Comp. 35 (1980), 1063-1079 Request permission

## Abstract:

Let ${\Omega ^c}$ be the complementary of a bounded regular domain in ${{\mathbf {R}}^2}$ of boundary $\Gamma$. We consider the problem (1) $\left \{ {\begin {array}{*{20}{c}} {\Delta u = f;} & {{\text {in}}\;{\Omega ^c},} \\ {u{|_\Gamma } = {u_{0,}}} & {} \\ \end {array} } \right .$ 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) $\left \{ {\begin {array}{*{20}{c}} {\Delta u = f} \hfill & {{\text {in}}\;{\Omega _1},} \hfill \\ {u{|_\Gamma } = {u_0},} \hfill & {} \hfill \\ {u{|_{{\Gamma _2}}} = \lambda .} \hfill & {} \hfill \\ \end {array} } \right .$ We introduce a finite element approximation of Eq. (2) and of the integral equation and we prove optimal error estimates.
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