### Symmetric Complex Boundary Element Scheme for 2-D Stokes Mixed Boundary Value Problem

*Sun-Gwon Hong*

#### Abstract

For 2-D Stokes mixed boundary value problems we construct a boundary

integral equation which couples a conventional boundary integral equation

for the velocity with a hypersingular boundary integral equation for the

traction. Expressing terms in the equation by complex variables, we obtain a

complex boundary integral equation and realize symmetrization of boundary

element scheme by Galerkin method. Applying a boundary limit method, we

obtain exact calculation formulae for calculation of hypersingular boundary

integrals. It is shown that all divergent terms in hypersingular integrals

cancel each other out.

integral equation which couples a conventional boundary integral equation

for the velocity with a hypersingular boundary integral equation for the

traction. Expressing terms in the equation by complex variables, we obtain a

complex boundary integral equation and realize symmetrization of boundary

element scheme by Galerkin method. Applying a boundary limit method, we

obtain exact calculation formulae for calculation of hypersingular boundary

integrals. It is shown that all divergent terms in hypersingular integrals

cancel each other out.

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