static void exact_sol(double x, double y, scalar& u0, scalar& u1, scalar& u1dx, scalar& u0dy)
{
scalar dx,dy;
u0 = exact0(x,y,dx,dy);
u1 = exact1(x,y,dx,dy);
scalar Hr = der_Hr(x,y);
scalar Ht = der_Ht(x,y);
scalar Hrr = der_Hrr(x,y);
scalar Hrt = der_Hrt(x,y);
scalar Htr = der_Htr(x,y);
scalar Htt = der_Htt(x,y);
double r = sqrt(x*x + y*y);
double theta = atan2(y,x);
scalar i = cplx(0.0,1.0);
u1dx = i * (( Hrr * x/r + Hrt * (-y/(r*r))) * x/r + Hr * (y*y)/(r*r*r) -
((Htr * x/r + Htt * (-y/(r*r))) * y/(r*r) + Ht * (-2.0*x*y/(r*r*r*r))));
u0dy = -i * (( Hrr * y/r + Hrt * x/(r*r)) * y/r + Hr * (x*x)/(r*r*r) +
(Htr * y/r + Htt * x/(r*r)) * x/(r*r) + Ht * (-2.0*x*y/(r*r*r*r)));
}
cplx bc_values(int marker, double x, double y)
{
scalar dx, dy;
return exact0(x, y, dx, dy)*tau[marker][0] + exact1(x, y, dx, dy)*tau[marker][1];
}
void test01 ( )
/******************************************************************************/
/*
Purpose:
TEST01 carries out test case #1.
Discussion:
Use A1, C1, F1, EXACT1, EXACT_UX1.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
14 June 2014
Author:
John Burkardt
Reference:
Dianne O'Leary,
Scientific Computing with Case Studies,
SIAM, 2008,
ISBN13: 978-0-898716-66-5,
LC: QA401.O44.
*/
{
int i;
int n = 11;
double e1;
double e2;
double h1s;
double *u;
double uexact;
double *x;
double x_first;
double x_last;
printf ( "\n" );
printf ( "TEST01\n" );
printf ( " Solve -( A(x) U'(x) )' + C(x) U(x) = F(x)\n" );
printf ( " for 0 < x < 1, with U(0) = U(1) = 0.\n" );
printf ( " A1(X) = 1.0\n" );
printf ( " C1(X) = 0.0\n" );
printf ( " F1(X) = X * ( X + 3 ) * exp ( X )\n" );
printf ( " U1(X) = X * ( 1 - X ) * exp ( X )\n" );
printf ( "\n" );
printf ( " Number of nodes = %d\n", n );
/*
Geometry definitions.
*/
x_first = 0.0;
x_last = 1.0;
x = r8vec_even_new ( n, x_first, x_last );
u = fem1d_bvp_linear ( n, a1, c1, f1, x );
printf ( "\n" );
printf ( " I X U Uexact Error\n" );
printf ( "\n" );
for ( i = 0; i < n; i++ )
{
uexact = exact1 ( x[i] );
printf ( " %4d %8f %14f %14f %14e\n",
i, x[i], u[i], uexact, fabs ( u[i] - uexact ) );
}
e1 = l1_error ( n, x, u, exact1 );
e2 = l2_error_linear ( n, x, u, exact1 );
h1s = h1s_error_linear ( n, x, u, exact_ux1 );
printf ( "\n" );
printf ( " l1 norm of error = %g\n", e1 );
printf ( " L2 norm of error = %g\n", e2 );
printf ( " Seminorm of error = %g\n", h1s );
free ( u );
free ( x );
return;
}
