NIST-01 (Analytic Solution)¶

Git reference: Benchmark nist-01.

The purpose of this benchmark is to observe how an adaptive algorithm behaves in a context where adaptivity isn’t really needed (smooth solution).

Model problem¶

Equation solved: Poisson equation

(1)-\Delta u = f.

Domain of interest: Unit Square (0, 1)^2.

Boundary conditions: Dirichlet, given by exact solution.

Exact solution¶

u(x,y) = 2^{4p}x^{p}(1-x)^{p}y^{p}(1-y)^p

where parameter p determines the degree of the polynomial solution.

Right-hand side: Obtained by inserting the exact solution into the latter equation. The corresponding code snippet is shown below:

{
public:
  CustomRightHandSide(double pol_deg)
    : DefaultNonConstRightHandSide(), pol_deg(pol_deg) {};

  virtual double value(double x, double y) const {
    double a = pow(2.0, 4.0*pol_deg);
    double b = pow(x-1.0, 8.0);
    double c = (38.0*pow(x, 2.0) - 38.0*x + 9.0);
    double d = pow(y-1.0, pol_deg);
    double e = pow(y-1.0, 8.0);
    double f = (38.0*pow(y, 2.0) - 38.0*y + 9.0);
    double g = pow(x-1.0, pol_deg);

    return -(pol_deg*a*pow(x, 8.0)*b*c*pow(y, pol_deg)*d
         + pol_deg*a*pow(y, 8.0)*e*f*pow(x, pol_deg)*g);
}