<commit_before>/* $Id$ */

/* The Next Great Finite Element Library. */
/* Copyright (C) 2004  <NAME>, <NAME> */

/* This library is free software; you can 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. */

/* This library is distributed in the hope that it will be useful, */
/* but WITHOUT ANY WARRANTY; without even the implied warranty of */
/* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU */
/* Lesser General Public License for more details. */

/* You should have received a copy of the GNU Lesser General Public */
/* License along with this library; if not, write to the Free Software */
/* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA */

 // <h1>Example 15 - Biharmonic Equation</h1>
 //
 // This example solves the Biharmonic equation on a square or cube,
 // using a Galerkin formulation with C1 elements approximating the
 // H^2_0 function space.
 // The initial mesh contains two TRI6, one QUAD9 or one HEX27
 // An input file named "ex15.in"
 // is provided which allows the user to set several parameters for
 // the solution so that the problem can be re-run without a
 // re-compile.  The solution technique employed is to have a
 // refinement loop with a linear solve inside followed by a
 // refinement of the grid and projection of the solution to the new grid
 // In the final loop iteration, there is no additional
 // refinement after the solve.  In the input file "ex15.in", the variable
 // "max_r_steps" controls the number of refinement steps, and
 // "max_r_level" controls the maximum element refinement level.

// LibMesh include files.
#include "mesh.h"
#include "equation_systems.h"
#include "linear_implicit_system.h"
#include "exodusII_io.h"
#include "fe.h"
#include "quadrature.h"
#include "dense_matrix.h"
#include "dense_vector.h"
#include "sparse_matrix.h"
#include "mesh_generation.h"
#include "mesh_modification.h"
#include "mesh_refinement.h"
#include "error_vector.h"
#include "fourth_error_estimators.h"
#include "getpot.h"
#include "exact_solution.h"
#include "dof_map.h"
#include "numeric_vector.h"
#include "elem.h"
#include "tensor_value.h"

// Bring in everything from the libMesh namespace
using namespace libMesh;

// Function prototype.  This is the function that will assemble<commit_msg>Adding another missing header<commit_after>/* $Id$ */

/* The Next Great Finite Element Library. */
/* Copyright (C) 2004  <NAME>, <NAME> */

/* This library is free software; you can 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. */

/* This library is distributed in the hope that it will be useful, */
/* but WITHOUT ANY WARRANTY; without even the implied warranty of */
/* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU */
/* Lesser General Public License for more details. */

/* You should have received a copy of the GNU Lesser General Public */
/* License along with this library; if not, write to the Free Software */
/* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA */

 // <h1>Example 15 - Biharmonic Equation</h1>
 //
 // This example solves the Biharmonic equation on a square or cube,
 // using a Galerkin formulation with C1 elements approximating the
 // H^2_0 function space.
 // The initial mesh contains two TRI6, one QUAD9 or one HEX27
 // An input file named "ex15.in"
 // is provided which allows the user to set several parameters for
 // the solution so that the problem can be re-run without a
 // re-compile.  The solution technique employed is to have a
 // refinement loop with a linear solve inside followed by a
 // refinement of the grid and projection of the solution to the new grid
 // In the final loop iteration, there is no additional
 // refinement after the solve.  In the input file "ex15.in", the variable
 // "max_r_steps" controls the number of refinement steps, and
 // "max_r_level" controls the maximum element refinement level.

// LibMesh include files.
#include "mesh.h"
#include "equation_systems.h"
#include "linear_implicit_system.h"
#include "exodusII_io.h"
#include "fe.h"
#include "quadrature.h"
#include "dense_matrix.h"
#include "dense_vector.h"
#include "sparse_matrix.h"
#include "mesh_generation.h"
#include "mesh_modification.h"
#include "mesh_refinement.h"
#include "error_vector.h"
#include "fourth_error_estimators.h"
#include "getpot.h"
#include "exact_solution.h"
#include "dof_map.h"
#include "numeric_vector.h"
#include "elem.h"
#include "tensor_value.h"
#include "perf_log.h"

// Bring in everything from the libMesh namespace
using namespace libMesh;

// Function prototype.  This is the function that will assemble
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