Index

NAME

ElmB4n2D - definition of 2D bilinear finite element

INCLUDE

include "ElmDefs.h"

SYNTAX

 class ElmB4n2D : public ElmTensorProd
 {
 public:
   ElmB4n2D ();
  ~ElmB4n2D () {}

   // efficient version:
   virtual void geomtFunc (Vec(real)& N, const Ptv(real)& loc_pt) const;
   virtual void dLocGeomtFunc (Mat(real)& dNloc, const Ptv(real)& loc_pt) const;
   virtual void d2LocBasisFunc(ArrayGen(real)& d2Nloc, const Ptv(real)& loc_pt)
      const;

   static void   shape (Vec(real)&        N,    const Ptv(real)& loc_pt);
   static void  dshape (Mat(real)&       dNloc, const Ptv(real)& loc_pt);
   static void d2shape (ArrayGen(real)& d2Nloc, const Ptv(real)& loc_pt);

   virtual bool findLocPt     // find local pt corresponding to global pt
     (
      const Ptv(real)& globpt,   // global pt
            Ptv(real)& locpt,    // local pt (output)
            int&       niter,    // no of Newton iterations in algorithm
            real&      error,    // error from the Newton iteration
      const Mat(real)& coor      // global coordinates of the nodes
     );

   virtual void drawElement
     (
      const Mat(real)&   coor,           // global, nodal coordinates
            GraphBasics& plotter,        // graphics: data, functions, dvi-code
            int          resolution = 1  // no of line segments along an edge
     )const;

   CLASS_INFO
 };

KEYWORDS

finite element, bilinear 2D element, Lagrange element family

DESCRIPTION

The  class  is derived from class ElmTensorProd and restricts the
interpolation to be of order one and the number of  space  dimen­
sions  to  equal  two.  That is, this is the standard 2D bilinear
quadrilateral finite element with 4 nodes.   Since  the  geometry
and  basis  functions  are hardcoded for this particular element,
geomtFunc and basisFunc are more efficient than the corresponding
functions in ElmTensorProd1.

Most  of  the operations on this element type are defined through
virtual functions or member functions of the base  class  ElmDef.
See  the documentation of class ElmDef for further explanation of
the interface. Some of the functions defined in base classes  may
be  found  reimplemented in this class in order to increase effi­
ciency by taking advantage of the information on  the  interpola­
tion order and the number of space dimensions.

CONSTRUCTORS AND INITIALIZATION

The only constructor performs all the initialization.

SEE ALSO

class ElmDef, class ElmTensorProd

DEVELOPED BY

SINTEF Applied Mathematics, Oslo, Norway, and University of Oslo,
Dept. of Mathematics, Norway

AUTHOR

Hans Petter Langtangen, SINTEF/UiO, additions by Klas Samuelsson,
UiO