Boundary element method for solving an inhomogeneous biharmonic equation with a right-hand side containing the unknown function and its derivatives

A boundary element method is proposed for solving an inhomogeneous biharmonic equation with a right-hand side containing the sought function and its derivatives. The accuracy of numerical results obtained for a test problem is analyzed by comparing them with its analytical solution. The flow through a porous medium with a nonuniform permeability distribution based on the Brinkman model is computed.