laphi instantiated
fem_check24_la.java running  
Given:
uy+uxxxx+uxx-ux=-cos(x)-sin(y)
xmin<=x<=xmax ymin<=y<=ymax Boundaries  
Analytic solution u(x,y)=sin(x)+cos(y)
xmin=0.0, xmax=1.0, ymin=0.0, ymax=1.0
nx=9, ny=9
x grid and analytic solution at ymin  
i=0, Ua(0.0)=1.0
i=1, Ua(0.125)=1.1246747333852276
i=2, Ua(0.25)=1.247403959254523
i=3, Ua(0.375)=1.3662725290860476
i=4, Ua(0.5)=1.479425538604203
i=5, Ua(0.625)=1.5850972729404622
i=6, Ua(0.75)=1.681638760023334
i=7, Ua(0.875)=1.767543502236027
i=8, Ua(1.0)=1.8414709848078965
 
y grid and analytic solution at xmin 
ii=0, Ua(0.0)=1.0
ii=1, Ua(0.125)=0.992197667229329
ii=2, Ua(0.25)=0.9689124217106447
ii=3, Ua(0.375)=0.9305076219123143
ii=4, Ua(0.5)=0.8775825618903728
ii=5, Ua(0.625)=0.8109631195052179
ii=6, Ua(0.75)=0.7316888688738209
ii=7, Ua(0.875)=0.6409968581633252
ii=8, Ua(1.0)=0.5403023058681398
 
 
boundary i=0,x=0.0, ii=0,y=0.0 is 1.0
boundary i=0,x=0.0, ii=8,y=1.0 is 0.5403023058681398
boundary i=1,x=0.125, ii=0,y=0.0 is 1.1246747333852276
boundary i=1,x=0.125, ii=8,y=1.0 is 0.6649770392533675
boundary i=2,x=0.25, ii=0,y=0.0 is 1.247403959254523
boundary i=2,x=0.25, ii=8,y=1.0 is 0.7877062651226627
boundary i=3,x=0.375, ii=0,y=0.0 is 1.3662725290860476
boundary i=3,x=0.375, ii=8,y=1.0 is 0.9065748349541873
boundary i=4,x=0.5, ii=0,y=0.0 is 1.479425538604203
boundary i=4,x=0.5, ii=8,y=1.0 is 1.0197278444723428
boundary i=5,x=0.625, ii=0,y=0.0 is 1.5850972729404622
boundary i=5,x=0.625, ii=8,y=1.0 is 1.125399578808602
boundary i=6,x=0.75, ii=0,y=0.0 is 1.681638760023334
boundary i=6,x=0.75, ii=8,y=1.0 is 1.2219410658914738
boundary i=7,x=0.875, ii=0,y=0.0 is 1.767543502236027
boundary i=7,x=0.875, ii=8,y=1.0 is 1.3078458081041668
boundary i=8,x=1.0, ii=0,y=0.0 is 1.8414709848078965
boundary i=8,x=1.0, ii=8,y=1.0 is 1.3817732906760363
boundary i=0,x=0.0, ii=0,y=0.0 is 1.0
boundary i=8,x=1.0, ii=0,y=0.0 is 1.8414709848078965
boundary i=0,x=0.0, ii=1,y=0.125 is 0.992197667229329
boundary i=8,x=1.0, ii=1,y=0.125 is 1.8336686520372254
boundary i=0,x=0.0, ii=2,y=0.25 is 0.9689124217106447
boundary i=8,x=1.0, ii=2,y=0.25 is 1.8103834065185413
boundary i=0,x=0.0, ii=3,y=0.375 is 0.9305076219123143
boundary i=8,x=1.0, ii=3,y=0.375 is 1.7719786067202108
boundary i=0,x=0.0, ii=4,y=0.5 is 0.8775825618903728
boundary i=8,x=1.0, ii=4,y=0.5 is 1.7190535466982693
boundary i=0,x=0.0, ii=5,y=0.625 is 0.8109631195052179
boundary i=8,x=1.0, ii=5,y=0.625 is 1.6524341043131145
boundary i=0,x=0.0, ii=6,y=0.75 is 0.7316888688738209
boundary i=8,x=1.0, ii=6,y=0.75 is 1.5731598536817173
boundary i=0,x=0.0, ii=7,y=0.875 is 0.6409968581633252
boundary i=8,x=1.0, ii=7,y=0.875 is 1.4824678429712217
boundary i=0,x=0.0, ii=8,y=1.0 is 0.5403023058681398
boundary i=8,x=1.0, ii=8,y=1.0 is 1.3817732906760363
calling gauleg xmin=0.0, xmax=1.0, npx=9
xx[1]=0.015919880246186957, xx[2]=0.08198444633668206, wx[1]=0.04063719418078437, wx[2]=0.09032408034742878
calling gauleg ymin=0.0, ymax=1.0, npy=9
yy[1]=0.015919880246186957, yy[2]=0.08198444633668206, wy[1]=0.04063719418078437, wy[2]=0.09032408034742878
galk(xx[2],yy[2])=-521992.81064135046
galf(xx[2],yy[2])=-2.372475818134688
compute stiffness matrix  
k computed stiffness matrix, see above  
f computed forcing function, see above  
ug computed Galerkin, Ua analytic, error  
ug[0,0]=1.000000000000013, Ua=1.0, err=1.3100631690576847E-14
ug[0,1]=0.9921976672293282, Ua=0.992197667229329, err=-7.771561172376096E-16
ug[0,2]=0.9689124217106221, Ua=0.9689124217106447, err=-2.2648549702353193E-14
ug[0,3]=0.9305076219122795, Ua=0.9305076219123143, err=-3.47499806707674E-14
ug[0,4]=0.8775825618903718, Ua=0.8775825618903728, err=-9.992007221626409E-16
ug[0,5]=0.8109631195052166, Ua=0.8109631195052179, err=-1.3322676295501878E-15
ug[0,6]=0.7316888688738428, Ua=0.7316888688738209, err=2.1871393585115584E-14
ug[0,7]=0.6409968581633116, Ua=0.6409968581633252, err=-1.354472090042691E-14
ug[0,8]=0.5403023058681398, Ua=0.5403023058681398, err=0.0
ug[1,0]=1.1246747333851637, Ua=1.1246747333852276, err=-6.394884621840902E-14
ug[1,1]=1.1284237499569088, Ua=1.1168724006145567, err=0.011551349342352024
ug[1,2]=1.1089932824124276, Ua=1.0935871550958725, err=0.015406127316555107
ug[1,3]=1.0717039326105464, Ua=1.055182355297542, err=0.01652157731300452
ug[1,4]=1.0125680237620855, Ua=1.0022572952756004, err=0.010310728486485177
ug[1,5]=0.9520775615965107, Ua=0.9356378528904457, err=0.016439708706065037
ug[1,6]=0.8717086672401848, Ua=0.8563636022590486, err=0.015345064981136192
ug[1,7]=0.7770949447170992, Ua=0.7656715915485529, err=0.011423353168546257
ug[1,8]=0.6649770392533675, Ua=0.6649770392533675, err=0.0
ug[2,0]=1.2474039592545243, Ua=1.247403959254523, err=1.3322676295501878E-15
ug[2,1]=1.2596310527211756, Ua=1.2396016264838519, err=0.020029426237323733
ug[2,2]=1.2430544901616258, Ua=1.2163163809651676, err=0.02673810919645825
ug[2,3]=1.2065738233161625, Ua=1.1779115811668373, err=0.028662242149325223
ug[2,4]=1.1428928119065063, Ua=1.1249865211448957, err=0.017906290761610544
ug[2,5]=1.0869383049102126, Ua=1.0583670787597408, err=0.028571226150471807
ug[2,6]=1.0057548095388427, Ua=0.9790928281283439, err=0.026661981410498803
ug[2,7]=0.9082841245896134, Ua=0.8884008174178482, err=0.01988330717176523
ug[2,8]=0.7877062651226627, Ua=0.7877062651226627, err=0.0
ug[3,0]=1.3662725290860303, Ua=1.3662725290860476, err=-1.7319479184152442E-14
ug[3,1]=1.3837152734004121, Ua=1.3584701963153765, err=0.02524507708503565
ug[3,2]=1.368916573063018, Ua=1.3351849507966924, err=0.033731622266325534
ug[3,3]=1.3329245280190918, Ua=1.2967801509983619, err=0.03614437702072992
ug[3,4]=1.266459092017044, Ua=1.2438550909764203, err=0.022604001040623656
ug[3,5]=1.213328772079052, Ua=1.1772356485912656, err=0.03609312348778637
ug[3,6]=1.131634140379873, Ua=1.0979613979598684, err=0.03367274242000473
ug[3,7]=1.032424766245697, Ua=1.0072693872493728, err=0.02515537899632414
ug[3,8]=0.9065748349541873, Ua=0.9065748349541873, err=0.0
ug[4,0]=1.4794255386042032, Ua=1.479425538604203, err=2.220446049250313E-16
ug[4,1]=1.4986969373999983, Ua=1.4716232058335321, err=0.027073731566466197
ug[4,2]=1.4845459409527102, Ua=1.4483379603148476, err=0.03620798063786257
ug[4,3]=1.4487154858586564, Ua=1.4099331605165173, err=0.0387823253421391
ug[4,4]=1.3812866418371073, Ua=1.3570081004945758, err=0.02427854134253149
ug[4,5]=1.3291835854234932, Ua=1.2903886581094208, err=0.038794927314072414
ug[4,6]=1.2472987529484953, Ua=1.211114407478024, err=0.036184345470471335
ug[4,7]=1.1475005429999783, Ua=1.1204223967675282, err=0.027078146232450084
ug[4,8]=1.0197278444723428, Ua=1.0197278444723428, err=0.0
ug[5,0]=1.5850972729404524, Ua=1.5850972729404622, err=-9.769962616701378E-15
ug[5,1]=1.6027457724098308, Ua=1.577294940169791, err=0.025450832240039745
ug[5,2]=1.5880780301133797, Ua=1.554009694651107, err=0.034068335462272614
ug[5,3]=1.552080961400634, Ua=1.5156048948527765, err=0.0364760665478574
ug[5,4]=1.4855378984398158, Ua=1.462679834830835, err=0.022858063608980794
ug[5,5]=1.4326115871143656, Ua=1.3960603924456803, err=0.036551194668685394
ug[5,6]=1.350869334044262, Ua=1.316786141814283, err=0.03408319222997891
ug[5,7]=1.2516433850905742, Ua=1.2260941311037874, err=0.025549253986786757
ug[5,8]=1.125399578808602, Ua=1.125399578808602, err=0.0
ug[6,0]=1.681638760023334, Ua=1.681638760023334, err=0.0
ug[6,1]=1.6942024962866924, Ua=1.6738364272526631, err=0.020366069034029266
ug[6,2]=1.6778375335942144, Ua=1.6505511817339789, err=0.027286351860235536
ug[6,3]=1.6413496379266803, Ua=1.6121463819356485, err=0.029203255991031796
ug[6,4]=1.577540539454958, Ua=1.5592213219137068, err=0.01831921754125121
ug[6,5]=1.521915842256817, Ua=1.492601879528552, err=0.02931396272826503
ug[6,6]=1.4406555897415956, Ua=1.413327628897155, err=0.027327960844440558
ug[6,7]=1.3431558551919807, Ua=1.3226356181866592, err=0.020520237005321462
ug[6,8]=1.2219410658914738, Ua=1.2219410658914738, err=0.0
ug[7,0]=1.767543502236027, Ua=1.767543502236027, err=0.0
ug[7,1]=1.771597839098149, Ua=1.759741169465356, err=0.011856669632793082
ug[7,2]=1.7523555362463696, Ua=1.736455923946672, err=0.01589961229969772
ug[7,3]=1.715061031485675, Ua=1.6980511241483414, err=0.01700990733733354
ug[7,4]=1.6558073985355577, Ua=1.6451260641263998, err=0.010681334409157861
ug[7,5]=1.5956104604253483, Ua=1.5785066217412451, err=0.017103838684103145
ug[7,6]=1.5151735837701494, Ua=1.4992323711098479, err=0.015941212660301574
ug[7,7]=1.420530760087587, Ua=1.4085403603993523, err=0.011990399688234676
ug[7,8]=1.3078458081041668, Ua=1.3078458081041668, err=0.0
ug[8,0]=1.8414709848078965, Ua=1.8414709848078965, err=0.0
ug[8,1]=1.8336686520372254, Ua=1.8336686520372254, err=0.0
ug[8,2]=1.8103834065185413, Ua=1.8103834065185413, err=0.0
ug[8,3]=1.7719786067202108, Ua=1.7719786067202108, err=0.0
ug[8,4]=1.7190535466982693, Ua=1.7190535466982693, err=0.0
ug[8,5]=1.6524341043131145, Ua=1.6524341043131145, err=0.0
ug[8,6]=1.5731598536817173, Ua=1.5731598536817173, err=0.0
ug[8,7]=1.4824678429712217, Ua=1.4824678429712217, err=0.0
ug[8,8]=1.3817732906760363, Ua=1.3817732906760363, err=0.0
nx=9, ny=9, npx=9, npy=9
                  maxerr=0.038794927314072414, avgerr=0.014745108408338528