function [] = Tst()
% set up grid
gd=0.;
numElem=4;
eLen=0.25;
for i=1:numElem+1
    ndCrd(i)=gd;
    gd=gd+eLen;
end
for i=1:numElem
    elemNod(i,1)=i;
    elemNod(i,2)=i+1;
end
% initial level set
dpos=0.1;
for i=1:numElem+1
    lSet(i)=sign(ndCrd(i)-dpos)*abs(dpos-ndCrd(i));
end
% force vector BC
fVect=zeros(12,1);
for i=1:numElem
    if sign(lSet(elemNod(i,1)))~=sign(lSet(elemNod(i,2)))
        fVect(elemNod(i,1))= 1.;
        fVect(elemNod(i,2))= 1.;
    end
end
% solve for velocity vector
Af=zeros(numElem+1);
% Assemble 'Stiffness' Matrices
for i=1:numElem
    pos(1)=-1/sqrt(3);
    pos(2)=1/sqrt(3);
    AfL=zeros(2);
    AfLGLS=zeros(2);
    for j=1:2
        shp(1)=(1-pos(j))/2.;
        shp(2)=(1+pos(j))/2.;
        dshp(1)=-0.5;
        dshp(2)=0.5;
        rset=shp(1)*lSet(elemNod(i,1))+shp(2)*lSet(elemNod(i,2));
        dls=dshp(1)*lSet(elemNod(i,1))+dshp(2)*lSet(elemNod(i,2));
        AfL=AfL+shp'*sign(rset)*(dls*dshp);
        AfLGLS=AfLGLS+(dshp'*dls)*(1./abs(dls))*(dls*dshp);
    end
    for k=1:2;
        for j=1:2;
           Af(elemNod(i,j),elemNod(i,k))=Af(elemNod(i,j),elemNod(i,k))+AfL(j,k)+AfLGLS(j,k);
        end
    end
end

% Update level set
mMat=zeros(numElem+1);
mMatGLS=zeros(numElem+1);
f1=zeros(numElem+1,1);
f2=zeros(numElem+1,1);
f3=zeros(numElem+1,1);
for i=1:numElem
    pos(1)=-1/sqrt(3);
    pos(2)=1/sqrt(3); 
    mMatL=zeros(2);
    mMatGLSL=zeros(2);
    f1L=zeros(2,1);
    f2L=zeros(2,1);
    f3L=zeors(2,1);
    for j=1:2
        shp(1)=(1-pos(j))/2.;
        shp(2)=(1+pos(j))/2.;
        dshp(1)=-0.5;
        dshp(2)=0.5;    
        Floc=shp(1)*fVect(elemNod(i,1))+shp(2)*fVect(elemNod(i,2));
        rset=shp(1)*lSet(elemNod(i,1))+shp(2)*lSet(elemNod(i,2));
        dls=dshp(1)*lSet(elemNod(i,1))+dshp(2)*lSet(elemNod(i,2)); 
        mMatL=mMatL+shp'*shp;
        mMatGLS=mMatGLS+dshp'*(dls/abs(dls))*Floc*1.*shp;
        f1L=f1L+shp'*Floc*abs(dls);
        f2L=f2L+dshp'*(dls/abs(dls))*Floc*1.*Floc*abs(dls);
        vs=1.*((abs(0.1+Floc*abs(dls)))/(abs(Floc*abs(dls))+1.));
        f3L=f3L+vs*dshp'*dls;
    end
    for k=1:2;
        for j=1:2;
           mMat(elemNod(i,j),elemNod(i,k))=mMat(elemNod(i,j),elemNod(i,k))+mMatL(j,k);
           mMatGLS(elemNod(i,j),elemNod(i,k))=mMatGLS(elemNod(i,j),elemNod(i,k))+mMatGLSL(j,k);           
        end
        f1(elemNod(i,k))=f1(elemNod(i,k))+f1L(k);
        f2(elemNod(i,k))=f2(elemNod(i,k))+f2L(k);
        f3(elemNod(i,k))=f3(elemNod(i,k))+f3L(k);       
    end
end
dt=0.1;
lSet=lSet-(((mMat+mMatGLS)^-1)/dt)*(f1+f2+f3);
lSet