DRBEM for Cauchy convection-diffusion problems with variable coefficients
In this study we present a numerical technique based on the Dual Reciprocity Boundary Element Method (DRBEM) combined with the Tikhonov regularisation method, or with the Truncated Singular Value Decomposition (TSVD) method, in order to solve the Cauchy problem associated with the steady-state convection-diffusion equation with variable coefficients. This is an interesting problem from the practical point of view as it can be used to model certain water pollution problems. The numerical results obtained in the test examples investigated show that the Tikhonov regularisation method is very suitable for the smooth geometries considered, i.e. circular and annular domains, while for the non-smooth rectangular domain the TSVD method is preferable. The choice of the regularisation parameter and of the truncation parameter is based on the L-curve method.
drbem tikhonov regularisation tsvd cauchy problem convection-diffusion equation l-curve