## TL;DR
A PETSc block size of 1 on a matrix assembled from a basix enriched_element (for example the MINI element, P1 Lagrange plus bubble) is expected, not a bug in your code. Plain vector Lagrange elements are blocked, so the block size equals gdim (2 in 2D), but an enriched element concatenates sub-element dofmaps and reports block size 1. PETSc GAMG reads the matrix block size to find the degrees of freedom per grid point, so set it yourself with A.setBlockSize(gdim) right after building the problem and before the first solve().

The PETSc PCGAMG docs state the requirement this way:

```text
To obtain good performance for PCGAMG for vector valued problems you must call MatSetBlockSize() to indicate the number of degrees of freedom per grid point
```

### Step 1 - confirm where the block size comes from
```python
print("dofmap block size:", V.dofmap.bs)
print("matrix block size:", problem.A.getBlockSize())
```
Expected output: dofmap bs is 1 and matrix block size is 1 for the enriched element; for the plain vector P2 element both report 2.

### Step 2 - set the block size before the solve
```python
from dolfinx.fem.petsc import LinearProblem
problem = LinearProblem(a_ufl, L_ufl, petsc_options={"ksp_type": "gmres", "pc_type": "gamg"})
problem.A.setBlockSize(gdim)
problem.solve()
```
Success check: problem.A.getBlockSize() now returns gdim, and GAMG needs fewer iterations than the block size 1 run (compare with the ksp_converged_reason option).

### Step 3 - nested Stokes matrices: set it on the velocity block
```python
A00 = A_nest.getLocalSubMatrix(0, 0)
A00.setBlockSize(gdim)
```
Do this for each vector-valued diagonal block before the KSP is set up.

### When this applies
- Matrix assembled from basix.ufl.enriched_element in DOLFINx (MINI element or any enriched combination)
- Using PETSc GAMG (or hypre BoomerAMG nodal coarsening) on the vector block
- A.getBlockSize() returns 1 where you expected gdim

### When this does not apply
- Plain vector Lagrange, Nedelec, or Raviart-Thomas elements already report the right block size; leave them alone
- Scalar problems, where block size 1 is correct
- Matrices you built explicitly as BAIJ, where the block size is fixed at creation

### Compatibility
DOLFINx 0.10 and 0.11, petsc4py 3.2x, PETSc 3.2x, basix enriched_element. The setBlockSize workaround applies to any version where the dofmap reports bs 1.

### Variant phrasings
- MINI element PETSc block size 1
- GAMG slow on enriched element in dolfinx
- MatGetBlockSize returns 1 for a vector function space

### Root cause
basix reports block size 1 for enriched elements because the element is a concatenation of sub-elements rather than a single blocked element. DOLFINx builds the dofmap from that (V.dofmap.bs is 1), and the assembled PETSc matrix inherits block size 1. GAMG then treats every degree of freedom as scalar, which usually still converges but builds a weaker multigrid hierarchy on the velocity block.

### Edge cases
- Set the block size before the KSP is set up (before the first solve()); changing it later may have no effect.
- Inside each sub-element block the dofs are still grouped gdim-per-entity (vertices for the P1 part, cell interiors for the bubble part), so gdim is the right value, but it remains a heuristic grouping for GAMG rather than a true nodal layout.
- For even better GAMG performance, also provide the near null space (one constant vector per component) via MatSetNearNullSpace; the PCGAMG docs page describes both requirements.

Provenance: drafted from public thread https://fenicsproject.discourse.group/t/incorrect-petsc-mat-block-size-when-using-enriched-element/19805

## Provenance

Resolved from the public thread: https://fenicsproject.discourse.group/t/incorrect-petsc-mat-block-size-when-using-enriched-element/19805

---

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## Selected public attribution and original notices/references

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