// This a the rotating hill problem with one turn.// First 1/2 turn is a convection equation and second 1/2 a convection diffusionint kt=6;int kloop=5;int nbadap=5;bool inq=1;real tol=0.05;real tol2=1e-4;border a(t=0, 2*pi)     {    x = cos(t);    y = sin(t);  }; // the unit circlemesh th = buildmesh(a(70));                                 // triangulates the diskfespace Vh(th,P1);Vh u1 = y, u2 = -x;           // rotation velocityVh m11=0,m22=0,m12=0;         // to store the metric fieldVh vT;                        // to save the initial in big loopint i;Vh vv,vo,vp; // working  Finite element function func rhill=sqrt((x-0.3)^2 +(y-0.3)^2);func  hill = 1-tanh(30*(rhill-0.2));//func real hill(real r2)  { return 1-tanh(100*(r2-0.04));}Vh v = hill;//((x-0.3)^2 +(y-0.3)^2);     // initial conditionplot(v);vp=0;for (int i=0;i<nbadap;i++) {  th=adaptmesh(th,v,err=tol,inquire=inq);  v = hill;//((x-0.3)^2 +(y-0.3)^2);        real errl2= sqrt(int2d(th)(square(vp-v))) ;  vp=vp-v;        cout << " interation adp =" << i << "  err l2 = " << errl2        << " diff min = " << vp[].min << " max =" << vp[].max << endl       << " --------------- " << endl;   vp=v;  if (errl2  < tol2) break; } plot(th,wait=1);real dt = 0.17,t=0;                                                 // time stepvT[]=v[];real error;for ( i=0; i< 20/kt ; i++) {    real T=t;     vp=0;    for (int k=0;k<kloop;k++)     {       t=T; //  restart       v=vT; // interpolation       m11=0;m22=0;m12=0; // reset metric          adaptmesh(th,v,err=tol,metric=[m11[],m12[],m22[]],nomeshgeneration= true );  // warning change the order in version 1.28              cout << "m11  = " << m11[].min << " " << m11[].max << endl;       cout << "m22  = " << m22[].min << " " << m22[].max << endl;       cout << "m12  = " << m12[].min << " " << m12[].max << endl;               for (int j=0;j<kt;j++)        {          t = t+dt;          vo[]=v[];          v=convect([u1,u2],-dt,vo);                          // convect v by u1,u2, dt seconds, results in f          plot(v,cmm="convection: t="+t + ", min=" + v[].min + ", max=" +  v[].max,wait=0);          adaptmesh(th,v,err=tol,metric=[m11[],m12[],m22[]],nomeshgeneration= true);        }        th=adaptmesh(th,v,err=tol,metric=[m11[],m12[],m22[]]);        vo=0; //        plot(th,wait=1,cmm="k=" + k + ", t= " + t + " ,i= " + i );          real errl2= sqrt(int2d(th)(square(vp-v))) ;        cout << " interation " << k << "  err l2 = " << errl2 << " --------------- " <<endl;         vp=v;	error=errl2;        if (errl2  < tol2) break;     }     vT=v; };plot(th,v,wait=1);