Qualocation

The qualocation method for boundary integral equations on smooth curves is reviewed, with an emphasis on recent developments, including ‘second-generation’ qualocation rules and ‘tolerant qualocation’. Using smoothest splines and uniform meshes, this version of the qualocation method can achieve the same convergence order as the Galerkin method, with no additional smoothness requirement on the solution, for a wide range of boundary integral operators. Included are singular integral equations with nonconstant coefficients.