gihXj7kClnm8oXpqmArtsSutv wExzy!{|mAj^}n~Ar?mi{|mtpqh mz q n F Q N c N A q N ^ ^ Q Å _ E'U©X c }G IL _ cYO h E aKu OMETLob _ m _ W Lob _ I
φ(x, y) =
m X
ZD\ i
γi φi (x, y)
i=1
I(φ) = I
"
m X i=1
γi φi
#
"m #2 "m #2 X ∂φi X ∂φi 1 = p(x, y) (x, y) + q(x, y) (x, y) γi γi 2 ∂x ∂y Ω i=1 i=1 "m #2 m X X −r(x, y) γi φi (x, y) γi φi (x, y) dydx + f (x, y) i=1 i=1 "m #2 Z m X X 1 + −g2 (x, y) γi φi (x, y) + g1 (x, y) γi φi (x, y) dS. 2 S2 ZZ
Æ Loc Lob X b-W _em _Da F FIcc } _ W _Tm _ E a L3dYO"H IL O h c L _Tm E _Tm L I(φ) d _ J*FIcYOgrIW ∂I (φ) = 0 J(O k = 1, . . . , n m _ W Lob _'h Loc FpO"HKc L a L aKu FIb i=1
i=1
γ1 , . . . , γn
FIcYO"}TL 0 S
∂γk
}(NKFIH`NKF J(O F h FIb'FIc u F
J(O
Ac = b, c = [γ1 · · · γn ]T ,
dYOEGF h N O
Loc
A = [αij ] b = [βi ] ZZ ∂φj ∂φi ∂φj ∂φi αij = (x, y) (x, y) + q(x, y) (x, y) (x, y) p(x, y) ∂x ∂x ∂y ∂y Ω Z −r(x, y)φi (x, y)φj (x, y) dxdy + g1 (x, y)φi (x, y)φj (x, y)dS
i, j = 1, . . . , n
Loc
βi = −
S2
ZZ
f (x, y)φi (x, y)dxdy + Ω
Z
S2
g2 (x, y)φi (x, y)dS −
m X
αik γk .
k=n+1
c _ u F f H O h F*m NKF a d _ _gu H FIW c u _ H OgrIX cYO u L h Feh d _ h u L aKuu LoaK| u u HKLoh } _gu c Lo}Tu Lo|c 6}(NKFIH a _ u WYO"JMc Feh U©X c }Gm IL NKu Fe_ c FIc L rMF h c FDSí§ h _ dYu O d b'FIc LF O E b%O HKLo}TL c FIc L rMF c L F L L`F FIb'FIc L J(O'}DO FIH FqEGF N O O r }TL v Loc v F L O E%L aKu FIb u HKLo} _gu c Lo}TX T Sfd F ANKF i 6= j a F d _gu FIb-c d HpS LoJMH OgαrIX c ij
k
I=
a d H FIb'FIc L4E E%d HKLob'FIHKX
i=j
dYO m _ W Lob _
ZZ
p(x, y) Ω
I=
I=
ZZ
∂φi ∂φj (x, y) (x, y)dxdy ∂x ∂x
p(x, y)bik bjk dxdy, Tk
X ZZ
k, vi ∈Tk
Tk
p(x, y)b2ik dxdy.
i
j