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Function File: A = bim2a_axisymmetric_laplacian (mesh,epsilon,kappa)

Build the standard finite element stiffness matrix for a diffusion problem in cylindrical coordinates with axisymmetric configuration. Rotational symmetry is assumed with respect to be the vertical axis r=0. Only plane geometries that DO NOT intersect the symmetry axis are admitted. 

    |   ____                 _|____ 
    |  |    \               \ |    |
  z |  |     \  OK           \|    |   NO!
    |  |______\               |\___|
    |     r                   |

The equation taken into account is:

1/r * d(r * Fr)/dr + dFz/dz = f

with

F = [Fr, Fz]’ = - epsilon * kappa grad (u)

where epsilon is an element-wise constant scalar function, while kappa is a piecewise linear conforming scalar function.

See also: bim2a_axisymmetric_rhs, bim2a_axisymmetric_reaction, bim2a_axisymmetric_advection_diffusion, bim2a_laplacian, bim1a_laplacian, bim3a_laplacian.

Package: bim