A boundary integral method applied to a convection-diffusion problem (Q1964117)

The author studies boundary integral methods for solving the Dirichlet problem for singularly perturbed convection-diffusion equations in a polygonal domain which are transformed to Helmholtz equations. He formulates several boundary integral equations and obtaines estimates of the single-layer potential operator in dependence of the perturbation parameter. The convergence of Galerkin and Galerkin-Petrov discretizations is discussed and demonstrated using some numerical examples.