convergence_study3.cc

#include <cmath>
#include <fstream>
#include <iomanip>
 
#include "primal_dpg.h"
#include "ultraweak_dpg.h"
 
#define reflev 7
 
int main() {
  std::cout << "Convergence study 4: Primal DPG method, solution with a "
               "boundary layer\n";
  std::cout << "Solution develops a boundary layer at top and right edge. \n";
 
  std::vector<double> epsilon_values = {1, 0.5, 0.1, 0.05, 0.02, 0.01};
  const double b1 = 2.0;
  const double b2 = 1.0;
 
  for (const double eps : epsilon_values) {
    //------------------------
    // Specification of the BVP
    //------------------------
    // exact solution:
    auto u1_exact = [eps, b1](double x) -> double {
      return x + (std::exp(x * b1 / eps) - 1) / (1 - std::exp(b1 / eps));
    };
    auto u1_exact_grad = [eps, b1](double x) -> double {
      return 1 + b1 / eps * std::exp(x * b1 / eps) / (1 - std::exp(b1 / eps));
    };
    auto u1_exact_d2 = [eps, b1](double x) -> double {
      return b1 * b1 / (eps * eps) * std::exp(x * b1 / eps) /
             (1 - std::exp(b1 / eps));
    };
 
    auto u2_exact = [eps, b2](double y) -> double {
      return y + (std::exp(y * b2 / eps) - 1) / (1 - std::exp(b2 / eps));
    };
    auto u2_exact_grad = [eps, b2](double y) -> double {
      return 1 + b2 / eps * std::exp(y * b2 / eps) / (1 - std::exp(b2 / eps));
    };
    auto u2_exact_d2 = [eps, b2](double y) -> double {
      return b2 * b2 / (eps * eps) * std::exp(y * b2 / eps) /
             (1 - std::exp(b2 / eps));
    };
 
    auto u_exact = [&u1_exact, &u2_exact](const Eigen::Vector2d& x) -> double {
      return u1_exact(x[0]) * u2_exact(x[1]);
    };
    auto u_grad = [eps, &u1_exact, &u2_exact, &u1_exact_grad, &u2_exact_grad](
                      const Eigen::Vector2d& x) -> Eigen::Vector2d {
      return (Eigen::VectorXd(2) << u1_exact_grad(x[0]) * u2_exact(x[1]),
              u1_exact(x[0]) * u2_exact_grad(x[1]))
          .finished();
    };
 
    auto epsilon = [eps](const Eigen::Vector2d & /*x*/) -> double {
      return eps;
    };
    auto beta = [b1, b2](const Eigen::Vector2d & /*x*/) -> Eigen::Vector2d {
      return (Eigen::VectorXd(2) << b1, b2).finished();
    };
 
    auto f = [eps, b1, b2, &u1_exact, &u1_exact_grad, &u1_exact_d2, &u2_exact,
              &u2_exact_grad,
              &u2_exact_d2](const Eigen::Vector2d& x) -> double {
      return -eps * (u1_exact_d2(x[0]) * u2_exact(x[1]) +
                     u1_exact(x[0]) * u2_exact_d2(x[1])) +
             b1 * u1_exact_grad(x[0]) * u2_exact(x[1]) +
             b2 * u1_exact(x[0]) * u2_exact_grad(x[1]);
    };
    auto g = [](const Eigen::Vector2d & /*x*/) -> double { return 0.0; };
 
    // specification of degree and enrichement for the method
    int deg_p = 2;
    int delta_p = 1;
 
    //------------------------
    // run the convergence test
    //------------------------
    std::cout << "Running convergence tests on a triangular mesh  (eps= " << eps
              << ")\n";
    auto errors = projects::dpg::test::
        TestConververgencePrimalDPGConvectionDiffusionDirichletBVP(
            reflev, u_exact, u_grad, epsilon, beta, f, g, deg_p, delta_p,
            lf::base::RefEl::kTria());
 
    // output to a corresponding file
    std::string file_name = "cs3/" + std::to_string(eps);
    std::ofstream file(file_name);
    for (auto [dofs, h1error, errorestimator] : errors) {
      file << dofs << ", " << h1error << ", " << errorestimator << std::endl;
    }
    file.close();
  }
 
  return 0;
}