PDE Solver using a Finite Element/Finite Volume approach: bim1a_axisymmetric_laplacian

### Categories &

#### Functions List

###### Matrix assembly

- bim1a_advection_diffusion
- bim1a_advection_upwind
- bim1a_axisymmetric_advection_diffusion
- bim1a_axisymmetric_advection_upwind
- bim2a_advection_diffusion
- bim2a_advection_upwind
- bim2a_axisymmetric_advection_diffusion
- bim2a_axisymmetric_advection_upwind
- bim3a_advection_diffusion
- bim3a_osc_advection_diffusion
- bim1a_laplacian
- bim1a_axisymmetric_laplacian
- bim2a_laplacian
- bim2a_axisymmetric_laplacian
- bim3a_laplacian
- bim3a_osc_laplacian
- bim1a_reaction
- bim1a_axisymmetric_reaction
- bim2a_reaction
- bim2a_axisymmetric_reaction
- bim3a_reaction
- bim1a_rhs
- bim1a_axisymmetric_rhs
- bim2a_rhs
- bim2a_axisymmetric_rhs
- bim3a_rhs
- bim2a_boundary_mass
- bim2a_axisymmetric_boundary_mass
- bim3a_boundary_mass

###### Pre-processing and Post-processing computations

- bim2c_mesh_properties
- bim3c_mesh_properties
- bim2c_unknowns_on_side
- bim3c_unknowns_on_faces
- bim2c_pde_gradient
- bim3c_pde_gradient
- bim2c_global_flux
- bim3c_global_flux
- bim1c_elem_to_nodes
- bim2c_tri_to_nodes
- bim3c_tri_to_nodes
- bim2c_intrp
- bim3c_intrp
- bim1c_norm
- bim2c_norm
- bim3c_norm

###### Utilities

- bimu_bernoulli
- bimu_logm

### Function Reference: `bim1a_axisymmetric_laplacian`

Function File: A = bim1a_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 grids that DO NOT contain r=0 are admissible.

       |   |-------|   OK       |--|-----|   NO!
      r=0                         r=0

The equation taken into account is:

- 1/r * (r * epsilon * kappa ( u’ ))’ = f

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

See also: bim1a_axisymmetric_rhs, bim1a_axisymmetric_reaction, bim1a_axisymmetric_advection_diffusion, bim2a_laplacian, bim3a_laplacian

Source Code: bim1a_axisymmetric_laplacian