Galerkin-least square B-spline approach toward advection–diffusion equation

• The study uses weighted residual least squares method using cubic B-splines.
• A numerical scheme is developed to solve PDEs involving advection–diffusion type phenomenon.
• The validity of the scheme is tested with several model problems.
• Method is shown to be highly accurate and computationally efficient.
• Stability and error analysis are presented.

Advection–diffusion equation is one of the governing equations used for modeling solute transport processes and water quality in rivers, lakes, oceans and groundwater etc. To simulate this class of mathematical problems, a computational scheme based on weighted residual least squares method using cubic B-splines is developed in this paper. Moreover, some test cases and results obtained are discussed and compared with the available data. The suggested method is shown to be accurate enough through these test examples.