cpraveen

/* ---------------------------------------------------------------------
 *
 * Copyright (C) 2013 - 2020 by the deal.II authors
 *
 * This file is part of the deal.II library.
 *
 * The deal.II library is free software; you can use it, redistribute
 * it, and/or modify it under the terms of the GNU Lesser General
 * Public License as published by the Free Software Foundation; either
 * version 2.1 of the License, or (at your option) any later version.

cpraveen

"""
-Laplace(u) = 0                 in [-1/2,+1/2] x [0,1]
         u  = (1/pi)*atan2(y,x) on boundary
Experiments to try:
   0) Run test_adapt.py to see the effect of refining a triangle
   1) Set nstep=5 and refine_type='uniform' and run the code. See the solution
      using paraview. Copy conv.dat to conv1.dat
   2) Set nstep=20 and refine_type='adaptive' and run the code. See the solution
      using paraview. Copy conv.dat to conv2.dat
   3) Start matlab and run the matlab code conv.m to see the convergence of L2

cpraveen

"""
Solve
    Laplace(u) = 0 in unit circle
with 
    u = -y on the boundary
We use Lagrange multipliers to implement dirichlet bc. The stress on the boundary is computed by a post-processing step in the end. The scheme is explained in

Gunzburger and Hou
TREATING INHOMOGENEOUS ESSENTIAL BOUNDARY CONDITIONS IN FINITE ELEMENT METHODS AND THE CALCULATION OF BOUNDARY STRESSES
SIAM J. Num. Anal., vol. 20, no. 2, pp. 390-424, April 1992

cpraveen

#include <deal.II/base/quadrature_lib.h>
#include <deal.II/grid/tria.h>
#include <deal.II/grid/tria_iterator.h>
#include <deal.II/grid/tria_accessor.h>
#include <deal.II/grid/grid_generator.h>
#include <deal.II/grid/grid_in.h>
#include <deal.II/grid/grid_out.h>
#include <deal.II/grid/tria_boundary_lib.h>
#include <deal.II/grid/grid_generator.h>
#include <deal.II/grid/grid_tools.h>

cpraveen

#ifndef __PROBLEM_H__
#define __PROBLEM_H__


namespace SWM
{
   using namespace dealii;
   
   // Base class to define problem initial condition, etc.
   template <int dim>