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# LaTeX2HTML 95.1 (Fri Jan 20 1995)# Associate image original text (scrambled) with physical files.$key = q/{_inline}$[A_T]${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img69.gif">'; $key = q/{_inline}$overlineOmega${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img26.gif">'; $key = q/{}parbox[b]6.5cmConsiderthefollowingelement:mboxcurvedP2triangle.bigskipInthisstep,thenodes1to6andthevertexcoordinatesweregenerated.Inthefollowingstep,thecoordinatesofthemid-sidenodeswillbecalculated.bigskip{}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img105.gif">'; $key = q/{}(nu){}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img246.gif">'; $key = q/{figure}[htp]centersetlengthunitlength1mmpicture(80,80)(0,0)put(0,0)framebox(80,80)inputfig1picturecenter{figure}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img165.gif">'; $key = q/{_inline}$le${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img137.gif">'; $key = q/{_inline}$Gamma_o${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img271.gif">'; $key = q/{_inline}$Gamma_0${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img59.gif">'; $key = q/{_inline}$displaystyle[tildeA]=sum_TincalT_hmbox^t[B_T][A_T][B_T],${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img70.gif">'; $key = q/{}(xneq(x_p,y_p)){}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img182.gif">'; $key = q/{_inline}$rho=1${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img60.gif">'; $key = q/{_inline}$displaystyle[Du_h|_T]=[DP]{u_T}${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img49.gif">'; $key = q/{_inline}$TcapGamma=0${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img94.gif">'; $key = q/{_inline}$u_h${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img39.gif">'; $key = q/{_inline}$displaystylenu=fracUtimesLRe${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img247.gif">'; $key = q/{_inline}$[k]:${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img144.gif">'; $key = q/{_inline}$displaystyleleft.arraylNIVO=1VTG=mboxlargearrayright}mboxhspace1cmfortheRHSvector.${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img125.gif">'; $key = q/{_inline}$TcapGammaneq0${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img95.gif">'; $key = q/{_inline}$r_3${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img190.gif">'; $key = q/{figure}[htbp]hboxtohsizehssplotftroisdfig17.ps10cm10cmhss{figure}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img232.gif">'; $key = q/{_inline}$displaystyleD=fracEe^312(1-nu^2)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img208.gif">'; $key = q/{_inline}$tildeimath${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img37.gif">'; $key = q/{_inline}$inL^infty(Omega)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img10.gif">'; $key = q/{_inline}$^st${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img141.gif">'; $key = q/{_inline}$f^Gamma${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img149.gif">'; $key = q/{_inline}$(tildeN-N_h)times(tildeN-N_h)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img86.gif">'; $key = q/{_inline}$0.78exp-03${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img253.gif">'; $key = q/{_inline}$v_i=0${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img67.gif">'; $key = q/{_inline}$u_h|_T${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img46.gif">'; $key = q/{_inline}$displaystyle[tildeA];=;sum_TincalT_hmbox^t[B_T][A_T][B_T].${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img74.gif">'; $key = q/{_inline}$k_11${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img159.gif">'; $key = q/{figure}[htbp]centerframeboxinputfigpart3b.texcenter{figure}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img277.gif">'; $key = q/{_inline}$u=(x-x^3)(y-y^3)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img162.gif">'; $key = q/{_inline}$displaystyleleft.arraylNIVO=4VTG=mboxlargearrayright}mboxhspace1cmforthematrix,${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img124.gif">'; $key = q/{_inline}$Gamma=partialOmega${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img240.gif">'; $key = q/{_inline}$w_A${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img201.gif">'; $key = q/{_inline}${w_i}${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img80.gif">'; $key = q/{figure}[htbp]hboxtohsizehssplotftroisdfigex2.ps8cm8cmhss{figure}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img142.gif">'; $key = q/{_inline}$longrightarrow${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img278.gif">'; $key = q/{_inline}$tildev_tildeimath=0${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img54.gif">'; $key = q/{_inline}$psi=0${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img272.gif">'; $key = q/{}((x_p,y_p)){}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img185.gif">'; $key = q/{}(=0){}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img181.gif">'; $key = q/{_inline}$P_k${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img24.gif">'; $key = q/{picture}(107,107)(3,0)thinlinessetlengthunitlength0.5cmput(1.8,0.5)footnotesize1put(1.8,2.2)footnotesize6put(1.8,5.1)footnotesize5put(1.8,7)footnotesize4put(6.1,0.5)footnotesize2put(6.1,7)footnotesize3put(2.25,7.2)_inline$bullet$_inlineput(2.25,5.45)_inline$bullet$_inlineput(2.25,2.05)_inline$bullet$_inlineput(2.25,0.3)_inline$bullet$_inlineput(5.7,7.2)_inline$bullet$_inlineput(5.7,0.3)_inline$bullet$_inlinesetlengthunitlength1cmput(0,0)makebox(4,4)plotftroisdfigex1.ps4cm4cm%{picture}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img138.gif">'; $key = q/{_inline}$displaystyle{tildeu}=[tildeu_tildeimath,...,tildeu_tildeN-N_h,0,...,0]${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img42.gif">'; $key = q/{_inline}$displaystyleleft[arraycctildeA_11;SPM_amp;tildeA_120;SPM_amp;1arrayright];left[arraycU_1U_0arrayright];=;left[arrayctildeB_1U_0arrayright]${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img129.gif">'; $key = q/{}(Gamma_1){}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img196.gif">'; $key = q/{_inline}${tildev}${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img53.gif">'; $key = q/{figure}[htbp]hboxtohsizehssplotftroisdhelena.ps8cm8cmhss{figure}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img164.gif">'; $key = q/{_inline}$displaystyle{tildeu};=;[tildeu_1,tildeu_2,...,tildeu_tildeN-N_h,0,...,0]${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img82.gif">'; $key = q/{_inline}$2times1861${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img275.gif">'; $key = q/{picture}(105,95)(22,25)thinlinessetlengthunitlength0.5mmput(24,78)oval(30,10)put(74,78)oval(30,10)put(50,23)oval(30,10)put(24,78)framebox(0,0)bfTAEput(74,78)framebox(0,0)bfNDL1put(50,23)framebox(0,0)bfBput(28,45)framebox(44,15)bfASEMBVput(25,72)vector(2,-1)15put(75,72)vector(-2,-1)15put(50,42)vector(0,-1)10{picture}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img2.gif">'; $key = q/{_inline}$O_y${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img212.gif">'; $key = q/{_inline}$displaystyleVTG+a;=;VTG${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img111.gif">'; $key = q/{_inline}$vinV_h${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img66.gif">'; $key = q/{_inline}$calT_h${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img25.gif">'; $key = q/{_inline}$uinH^1_0(Omega)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img14.gif">'; $key = q/{figure}[htbp]hboxtohsizehssplotftroisdfig11.ps8cm8cmhss{figure}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img214.gif">'; $key = q/{_inline}$[tildeB]${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img115.gif">'; $key = q/{_inline}$displaystyle[A_T];=;[K_T]+a[M_T],${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img73.gif">'; $key = q/{_inline}$^o${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img251.gif">'; $key = q/{_inline}$vinH^1_0(Omega)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img16.gif">'; $key = q/{_inline}$displaystyle[DP]=left[arraycccdisplaystylefracpartialp_1partialx;SPM_amp;cdots;SPM_amp;displaystylefracpartialp_Npartialxdisplaystylefracpartialp_1partialy;SPM_amp;cdots;SPM_amp;displaystylefracpartialp_Npartialyarrayright]${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img50.gif">'; $key = q/{_inline}$foralltildeimathinN_h${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img55.gif">'; $key = q/{_inline}$S${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img284.gif">'; $key = q/{_inline}$1.10^5${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img209.gif">'; $key = q/{_inline}$(tildeN-N_h)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img90.gif">'; $key = q/{_inline}$Gamma_1${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img133.gif">'; $key = q/{_inline}$TincalT_h${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img93.gif">'; $key = q/{_inline}$[K_T]${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img154.gif">'; $key = q/{_inline}$vecu=(u_1,u_2)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img243.gif">'; $key = q/{_inline}$tildeu_tildeimath=0${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img51.gif">'; $key = q/{_inline}$displaystyleg=750.Wm^2C.${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img167.gif">'; $key = q/{_inline}$[tildeA_1]${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img92.gif">'; $key = q/{figure}[htbp]hboxtohsizehssplotftroisdfig2.ps8cm8cmhss{figure}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img169.gif">'; $key = q/{_inline}$10.0exp+05${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img193.gif">'; $key = q/{figure}[htp]centersetlengthunitlength1mmpicture(130,130)(0,0)put(0,0)framebox(130,130)put(10,120)Level5put(10,100)Level4put(10,80)Level3put(10,60)Level2put(10,40)Level1put(10,20)Level0put(60,95)framebox(30,10)Mainprogramsput(60,75)framebox(30,10)Modulesput(60,35)framebox(30,10)Fortran77put(60,15)framebox(30,10)Computerput(50,110)framebox(50,15)put(54,118)Mathematicalformulationput(57,113)ofthephysicalproblemput(35,55)framebox(35,10)Numericalalgorithmsput(85,55)framebox(30,10)Utilitiesput(90,100)vector(1,0)35put(90,80)vector(1,0)35put(125,40)vector(-1,0)35put(125,100)vector(0,-1)60put(75,110)vector(0,-1)5put(75,95)vector(0,-1)10put(75,35)vector(0,-1)10put(65,75)vector(-1,-1)10put(85,75)vector(1,-1)10put(55,55)vector(1,-1)10put(95,55)vector(-1,-1)10put(30,50)dashbox3(90,57)put(35,70)shortstackMODULEFpicturecenter{figure}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img3.gif">'; $key = q/{figure}[htbp]hboxtohsizehssplotftroisdfig4.ps8cm8cmhss{figure}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img174.gif">'; $key = q/{_inline}$w_i${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img44.gif">'; $key = q/{_inline}$u_hinV_0h${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img17.gif">'; $key = q/{_inline}$f^Omega=6xy(3-2x^2-2y^2+x^2y^2)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img158.gif">'; $key = q/{figure}[htbp]hboxtohsizehssplotftroisdfig6.ps8cm8cmhss{figure}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img198.gif">'; $key = q/{_inline}$displaystyleleft{arrayrclldisplaystylefracpartialvecupartialt+(vecu.nabla)vecu-nunablavecu+nablap;SPM_amp;=;SPM_amp;0;SPM_amp;mboxwhere;SPM_amp;;SPM_amp;;SPM_amp;mbox[(vecu.nabla)vecu]_i;SPM_amp;=;SPM_amp;displaystylesum_j=i^N;u_jfracpartialu_ipartialx_j;SPM_amp;i=1,ldots,NmboxTheincompressibilitycondition:;SPM_amp;;SPM_amp;;SPM_amp;displaystylenabla.vecu;SPM_amp;=;SPM_amp;0;SPM_amp;mboxTheboundarycondition:;SPM_amp;;SPM_amp;;SPM_amp;vecu|_Gamma;SPM_amp;=;SPM_amp;vecu_Gamma;SPM_amp;mboxTheinitialcondition:;SPM_amp;;SPM_amp;;SPM_amp;vecu(x,0);SPM_amp;=;SPM_amp;vecu_0(x);SPM_amp;arrayright.${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img241.gif">'; $key = q/{_inline}$vecv=0${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img270.gif">'; $key = q/{}(vecu_Gamma){}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img245.gif">'; 

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