Problem Statement   

      DE for 2-D, steady convection diffusion is

            DE:     

            BCs:     on ¶W (x,1) and (1,y)

                        q(x,0) = q(0,y) = 0

            data:     q(1,1) = 1, s = 0 

The Galerkin weak statement definition

            GWSN =

when implemented as GWSh via the linear FE basis leads to 

            {WS}e = (u,[ ],[ ],0,’B201L’,q)

                        +(v,[ ],[ ],0,’B202L’,q)

                        +(1/Pe,[ ],[ ],-1,’B211L’,q)

                        +(1/Pe,[ ],[ ],-1,’B212L’,q)

                        +(1/Pe,[ ],[ ],-1,’B221L’,q)

                        +(1/Pe,[ ],[ ],-1,’B222L’,q) 

      The TWSh augmentation to GWSh generates the “b-term,” and the steady state theory determines the form to be

            TWSh

Recall the Peclet number Pe is the product of Prandtl(Pr) and Reynolds(Re) number, which for practical engineering problems is large. Implementation of the TWS “b-term” adds the following to the GWSh {WS}e template syntax 

            +(h2Pe/12,[ ],[ ],-1,'B211L',q)

            +(h2Pe/12,[ ],[ ],-1,'B212L',q)

            +(h2Pe/12,[ ],[ ],-1,'B221L',q)

            +(h2Pe/12,[ ],[ ],-1,'B222L',q) 

where ‘h’ represents the length of the element for the uniform mesh.