Space L2 (05-space-l2)ΒΆ

The L2 space is used, for example, in `Navier-Stokes equations where it keeps the velocity discreetely divergence-free. This example shows how to create an L2 space, visualize finite element basis functions, and perform an orthogonal L2-projection of a continuous function onto the FE space.

First, an L2 space is created as the reader expects:

// Create an L2 space with default shapeset.
L2Space<double> space(&mesh, P_INIT);

The function to be projected is:

CustomExactSolution sln_exact(&mesh);

See formula in the file definitions.cpp. The projection is done as follows:

OGProjection<double> ogProjection; ogProjection.project_global(&space, &sln_exact, &sln);

Sample basis functions visualized using the BaseView class:

Sample basis function
Sample basis function
Sample basis function
Sample basis function

The projection (note that this is a discontinuous function):


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