laphi instantiated
fem_check22_la.java running  
Given:
uxx+2*uxy+3*uyy+4*ux+5*uy+6*u=f(x,y)
f(x,y)=6x^3+6y^3+12x^2+15y^2+6xy+11x+22y+8
xmin<=x<=xmax ymin<=y<=ymax Boundaries  
Analytic solution u(x,y)=x^3 + y^3 + xy + 1
xmin=0.0, xmax=1.0, ymin=0.0, ymax=1.0
nx=4, ny=4
x grid and analytic solution at ymin  
i=0, Ua(0.0)=1.0
i=1, Ua(0.3333333333333333)=1.037037037037037
i=2, Ua(0.6666666666666666)=1.2962962962962963
i=3, Ua(1.0)=2.0
 
y grid and analytic solution at xmin 
ii=0, Ua(0.0)=1.0
ii=1, Ua(0.3333333333333333)=1.037037037037037
ii=2, Ua(0.6666666666666666)=1.2962962962962963
ii=3, Ua(1.0)=2.0
 
solution at i=0,x=0.0, ii=0,y=0.0 is1.0
solution at i=0,x=0.0, ii=1,y=0.3333333333333333 is1.037037037037037
solution at i=0,x=0.0, ii=2,y=0.6666666666666666 is1.2962962962962963
solution at i=0,x=0.0, ii=3,y=1.0 is2.0
solution at i=1,x=0.3333333333333333, ii=0,y=0.0 is1.037037037037037
solution at i=1,x=0.3333333333333333, ii=1,y=0.3333333333333333 is1.1851851851851851
solution at i=1,x=0.3333333333333333, ii=2,y=0.6666666666666666 is1.5555555555555556
solution at i=1,x=0.3333333333333333, ii=3,y=1.0 is2.3703703703703702
solution at i=2,x=0.6666666666666666, ii=0,y=0.0 is1.2962962962962963
solution at i=2,x=0.6666666666666666, ii=1,y=0.3333333333333333 is1.5555555555555556
solution at i=2,x=0.6666666666666666, ii=2,y=0.6666666666666666 is2.037037037037037
solution at i=2,x=0.6666666666666666, ii=3,y=1.0 is2.962962962962963
solution at i=3,x=1.0, ii=0,y=0.0 is2.0
solution at i=3,x=1.0, ii=1,y=0.3333333333333333 is2.3703703703703702
solution at i=3,x=1.0, ii=2,y=0.6666666666666666 is2.962962962962963
solution at i=3,x=1.0, ii=3,y=1.0 is4.0
 
boundary i=0,x=0.0, ii=0,y=0.0 is 1.0
boundary i=0,x=0.0, ii=3,y=1.0 is 2.0
boundary i=1,x=0.3333333333333333, ii=0,y=0.0 is 1.037037037037037
boundary i=1,x=0.3333333333333333, ii=3,y=1.0 is 2.3703703703703702
boundary i=2,x=0.6666666666666666, ii=0,y=0.0 is 1.2962962962962963
boundary i=2,x=0.6666666666666666, ii=3,y=1.0 is 2.962962962962963
boundary i=3,x=1.0, ii=0,y=0.0 is 2.0
boundary i=3,x=1.0, ii=3,y=1.0 is 4.0
boundary i=0,x=0.0, ii=0,y=0.0 is 1.0
boundary i=3,x=1.0, ii=0,y=0.0 is 2.0
boundary i=0,x=0.0, ii=1,y=0.3333333333333333 is 1.037037037037037
boundary i=3,x=1.0, ii=1,y=0.3333333333333333 is 2.3703703703703702
boundary i=0,x=0.0, ii=2,y=0.6666666666666666 is 1.2962962962962963
boundary i=3,x=1.0, ii=2,y=0.6666666666666666 is 2.962962962962963
boundary i=0,x=0.0, ii=3,y=1.0 is 2.0
boundary i=3,x=1.0, ii=3,y=1.0 is 4.0
calling gauleg xmin=0.0, xmax=1.0, npx=6
xx[1]=0.033765242898423975, xx[2]=0.1693953067668677, wx[1]=0.08566224618958117, wx[2]=0.1803807865240693
calling gauleg ymin=0.0, ymax=1.0, npy=12
yy[1]=0.009219682876640378, yy[2]=0.0479413718147626, wy[1]=0.023587668193253912, wy[2]=0.05346966299765909
galk(xx[2],yy[2])=-19.597567969234152
galf(xx[2],yy[2])=4.096343135198095
compute stiffness matrix  
Legendre integration=1.7720184948979385, at i=1, j=0, ii=1, jj=0
Legendre integration=-1.0496938775509936, at i=1, j=0, ii=1, jj=1
Legendre integration=0.06069834183672094, at i=1, j=0, ii=1, jj=2
Legendre integration=0.05269132653061445, at i=1, j=0, ii=1, jj=3
Legendre integration=-0.6255229591836661, at i=1, j=0, ii=2, jj=0
Legendre integration=2.34967155612242, at i=1, j=0, ii=2, jj=1
Legendre integration=-1.0496938775509947, at i=1, j=0, ii=2, jj=2
Legendre integration=0.16125956632652236, at i=1, j=0, ii=2, jj=3
Legendre integration=3.5933418367346848, at i=1, j=1, ii=1, jj=0
Legendre integration=-15.770204081632572, at i=1, j=1, ii=1, jj=1
Legendre integration=10.953596938775446, at i=1, j=1, ii=1, jj=2
Legendre integration=-1.9588775510203948, at i=1, j=1, ii=1, jj=3
Legendre integration=-0.801734693877548, at i=1, j=1, ii=2, jj=0
Legendre integration=7.048239795918334, at i=1, j=1, ii=2, jj=1
Legendre integration=-15.770204081632563, at i=1, j=1, ii=2, jj=2
Legendre integration=6.341556122448943, at i=1, j=1, ii=2, jj=3
Legendre integration=-1.295328443877549, at i=1, j=2, ii=1, jj=0
Legendre integration=5.8766326530611845, at i=1, j=2, ii=1, jj=1
Legendre integration=0.19294323979591962, at i=1, j=2, ii=1, jj=2
Legendre integration=-0.5796045918367301, at i=1, j=2, ii=1, jj=3
Legendre integration=0.4907525510204072, at i=1, j=2, ii=2, jj=0
Legendre integration=-3.419512117346922, at i=1, j=2, ii=2, jj=1
Legendre integration=5.87663265306119, at i=1, j=2, ii=2, jj=2
Legendre integration=1.246769770408151, at i=1, j=2, ii=2, jj=3
Legendre integration=0.042244897959186685, at i=1, j=3, ii=1, jj=0
Legendre integration=-0.3388775510204105, at i=1, j=3, ii=1, jj=1
Legendre integration=-1.064158163265291, at i=1, j=3, ii=1, jj=2
Legendre integration=0.35632653061223996, at i=1, j=3, ii=1, jj=3
Legendre integration=-0.06795918367346995, at i=1, j=3, ii=2, jj=0
Legendre integration=0.3678061224489814, at i=1, j=3, ii=2, jj=1
Legendre integration=-0.3388775510204126, at i=1, j=3, ii=2, jj=2
Legendre integration=-0.9654336734693739, at i=1, j=3, ii=2, jj=3
Legendre integration=-0.6713265306122356, at i=2, j=0, ii=1, jj=0
Legendre integration=0.5868367346938657, at i=2, j=0, ii=1, jj=1
Legendre integration=0.03512755102041586, at i=2, j=0, ii=1, jj=2
Legendre integration=-0.05510204081632798, at i=2, j=0, ii=1, jj=3
Legendre integration=0.24061224489795605, at i=2, j=0, ii=2, jj=0
Legendre integration=-0.9629081632652939, at i=2, j=0, ii=2, jj=1
Legendre integration=0.5868367346938671, at i=2, j=0, ii=2, jj=2
Legendre integration=0.030994897959188777, at i=2, j=0, ii=2, jj=3
Legendre integration=1.1129751275510105, at i=2, j=1, ii=1, jj=0
Legendre integration=2.7523469387754886, at i=2, j=1, ii=1, jj=1
Legendre integration=-3.5171460459183534, at i=2, j=1, ii=1, jj=2
Legendre integration=0.8089668367346908, at i=2, j=1, ii=1, jj=3
Legendre integration=-0.5506760204081592, at i=2, j=1, ii=2, jj=0
Legendre integration=1.0716485969387737, at i=2, j=1, ii=2, jj=1
Legendre integration=2.7523469387754833, at i=2, j=1, ii=2, jj=2
Legendre integration=-2.1161766581632575, at i=2, j=1, ii=2, jj=3
Legendre integration=3.593341836734677, at i=2, j=2, ii=1, jj=0
Legendre integration=-15.770204081632558, at i=2, j=2, ii=1, jj=1
Legendre integration=10.953596938775464, at i=2, j=2, ii=1, jj=2
Legendre integration=-1.9588775510204015, at i=2, j=2, ii=1, jj=3
Legendre integration=-0.8017346938775438, at i=2, j=2, ii=2, jj=0
Legendre integration=7.048239795918315, at i=2, j=2, ii=2, jj=1
Legendre integration=-15.770204081632556, at i=2, j=2, ii=2, jj=2
Legendre integration=6.341556122448962, at i=2, j=2, ii=2, jj=3
Legendre integration=0.07728635204081119, at i=2, j=3, ii=1, jj=0
Legendre integration=1.1488775510204123, at i=2, j=3, ii=1, jj=1
Legendre integration=2.671501913265272, at i=2, j=3, ii=1, jj=2
Legendre integration=-0.9244515306122336, at i=2, j=3, ii=1, jj=3
Legendre integration=0.10733418367347013, at i=2, j=3, ii=2, jj=0
Legendre integration=-0.810774872448981, at i=2, j=3, ii=2, jj=1
Legendre integration=1.1488775510204172, at i=2, j=3, ii=2, jj=2
Legendre integration=2.5277774234693564, at i=2, j=3, ii=2, jj=3
Legendre integration=1.9904464285714236, f at i=1, ii=1
Legendre integration=5.647499999999977, f at i=1, ii=2
Legendre integration=4.466249999999976, f at i=2, ii=1
Legendre integration=8.427053571428527, f at i=2, ii=2
k computed stiffness matrix, see above  
f computed forcing function, see above  
ug computed Galerkin, Ua analytic, error  
ug[0,0]=0.9999999999999998, Ua=1.0, err=-2.220446049250313E-16
ug[0,1]=1.0370370370370385, Ua=1.037037037037037, err=1.5543122344752192E-15
ug[0,2]=1.2962962962962963, Ua=1.2962962962962963, err=0.0
ug[0,3]=2.0, Ua=2.0, err=0.0
ug[1,0]=1.037037037037037, Ua=1.037037037037037, err=0.0
ug[1,1]=1.185185185185187, Ua=1.1851851851851851, err=1.7763568394002505E-15
ug[1,2]=1.5555555555555562, Ua=1.5555555555555556, err=6.661338147750939E-16
ug[1,3]=2.3703703703703702, Ua=2.3703703703703702, err=0.0
ug[2,0]=1.2962962962962972, Ua=1.2962962962962963, err=8.881784197001252E-16
ug[2,1]=1.5555555555555562, Ua=1.5555555555555556, err=6.661338147750939E-16
ug[2,2]=2.0370370370370376, Ua=2.037037037037037, err=4.440892098500626E-16
ug[2,3]=2.962962962962963, Ua=2.962962962962963, err=0.0
ug[3,0]=2.0, Ua=2.0, err=0.0
ug[3,1]=2.3703703703703702, Ua=2.3703703703703702, err=0.0
ug[3,2]=2.962962962962963, Ua=2.962962962962963, err=0.0
ug[3,3]=4.0, Ua=4.0, err=0.0
                  maxerr=1.7763568394002505E-15, avgerr=3.885780586188048E-16