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

Sun-Gwon Hong


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.

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