Page 89 -
P. 89

K   )τ  ψ  V         −Dϕ    K   )ψ

                                                        −      =             =      +      ψ
                                                 Dϕ      2            K)ϕ           −( 1 I  2  −V
                                           K)ϕ   =      =( 1 I  v j, dsv j  +  v j, dsτ j,   =  =
                                           +     n  dsn        ·      =(− 1 I  2  ·
                                           =( 1 I  2    v j, dsv j,      u  Γ       τ  Γ    v j, dsv j,   n  dsn

                                   II      n  dsn       ·  τ  Γ    ·  u  3(n−1)     j=1  n  dsn    3(n−1)     j=1  ·  u     ·  u  Γ
                                   Equations     ·  τ  L     +   =1  3(n−1)       Γ   j=1  L     +   =1     ·  τ  Γ    L     +   =1  3(n−1)       Γ   j=1  L     +   =1




                                   Modified  L     +  τ  V   =1 Γ  K   )τ  −  ( 1 I  2  L     +  Du   =1  K)u  +  ( 1 I  2  L     +  τ  V   =1  K   )τ  −  ( 1 I  2  L     +  Du   =1  K)u  −  ( 1 I  2




                                                               =0
                                                               v j, ds


                                                               ·  u                        =0
                             Problems                   =0       =  Γ        =0  v j, ds  =0,  v j, ds  n  ds  ·  u



                             Stokes        =0    =0     v j, ds  ·  u  τ j, ds  V  ·  u  =0     ·  τ  Γ       ·  u  Γ       =  Γ

                             3–D   1)  −   n  ds  n  ds     and  Γ       Γ    n  ds  and  and  Du 0 ds

                             the   1, 3(n  ·  τ  ·  τ          and      ·  τ  −Dϕ   K   )ψ     ·  u  Γ
                             for   =        and  Γ       and  Γ    K   )ψ  −  ψ  V  =  and  Γ    =  +  and
                             Equations  j  1,L ,  K)ϕ  +  Dϕ  =  =( 1 I  2  ω j, v j,   K)ϕ  +  ω j, τ j,   −( 1 I  =  2  ψ  −V  =




                             Integral  =     I ,  =( 1 I  2         =1 ω  n    ω j, v j,   3(n−1)  L       j=1   =1  =(− 1 I  2  3(n−1)  L       j=1   =1  ω j, v j,   L      =1 ω  n


                             Modified  Equations  L     +   =1 ω  n    +  K   )τ  −  3(n−1)  L       +  j=1   =1  +  K)u  +  L     +   =1 ω  n    +  K   )τ  −  3(n−1)  L       +  j=1   =1  +  K)u  −



                             2.3.4.  Modified  τ  (1)V  (2)( 1 I  2  (1)Du  (2)( 1 I  2  τ  (1)V  (2)( 1 I  2  (1)Du  (2)( 1 I  2

                             Table

                                                IDP          INP           EDP           ENP
   84   85   86   87   88   89   90   91   92   93   94