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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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On the coupling of boundary integral and finite element methods
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by Claes Johnson and J.-Claude Nédélec PDF
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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Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Math. Comp. 35 (1980), 1063-1079
  • MSC: Primary 65N30
  • DOI: https://doi.org/10.1090/S0025-5718-1980-0583487-9
  • MathSciNet review: 583487