# 7.15.1.16. Projection

Syntax

  Eq [{Lumped_|Lagged_|Quasi_Implicit_}]Projection for Associated DoF [{of} SpeciesName | {in} MaterialPhaseName | {ls} {a | b | c}] {on} MeshPart using Interp with {Term_0} … {Term_N}

Scope

  Aria Region

Summary

  Perform a projection of an expression from integration points to nodal values.

Description

  The string Dof refers to a new degree of freedom to be created and solved for via the projection equation. Dof can be chosen to be any expression valid at the integration points, in which case the string used for Dof should be the decorated version of the original expression name. A prefix of `PROJECTED_`, `PROJECTED_VECTOR_`, and `PROJECTED_TENSOR_` should be used for scalar, vector, and tensor expressions, respectively.

  By default, projection equations use a consistent source term resulting in a formal L2 projection; however, projection equations can also use a lumped source term by specifying `LUMPED_` before `PROJECTION`. Projection equations are normally solved by the linear solver; however, they can be lagged and solved at the start of a time step by specifying `LAGGED_` or once per nonlinear iteration by specifying `QUASI_IMPLICIT_`. Using either the `LAGGED_` or `QUASI_IMPLICIT_` prefixes will not burden the linear solver, but explicit solution necessarily requires that both options use a lumped projection.

  Admissible values of Interp are .

  The only admissible value of Term_n is `DEF`.

  The Meshpart must be an active element block.

Example

  To project the heat conduction on every block using linear elements, one would use the command

      Eq Projection For Vector_Heat_Conduction On All_Blocks Using Q1 With Def

  Likewise, to project a mesh stress, one could specify

      Eq Projection For Projected_Tensor_Mesh_Stress On All_Blocks Using Q1 With Def

Parameter | Value | Default
--- | --- | ---
{of} | {of | species | subindex} | –
SpeciesName | string | –
{in} | {in | material_phase} | –
MaterialPhaseName | string | –
{ls} | {levelset_phase | ls} | –
Associated DoF | string | –
{on} | {@ | at | for | in | on | over} | –
MeshPart | string | –
Interp | string | –
{Term_n} | See Description | –