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Minor improvements to Bilinear Form Integrators page #310

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22 changes: 11 additions & 11 deletions src/bilininteg.md
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Expand Up @@ -92,7 +92,7 @@ Note that any operators involving a derivative of the range function
$v$ or $\vec\{v}$ are computed using integration by parts. This leads
to a boundary integral which can be used to apply Neumann boundary
conditions. Some of these operators are listed along with their
boundary terms in section [Weak Operators](#weak-operators-and-their-boundary-integrals).
boundary terms in section [Weak Operators and Their Boundary Integrals](#weak-operators-and-their-boundary-integrals).

## Scalar Field Operators

Expand All @@ -102,7 +102,7 @@ require a gradient operator should be used with H1.

### Square Operators

These integrators are designed to be used with the BilinearForm object
These integrators are designed to be used with a `BilinearForm` object
to assemble square linear operators.

| Class Name | Spaces | Coef.| Operator | Continuous Op. | Dimension |
Expand All @@ -112,7 +112,7 @@ to assemble square linear operators.

### Mixed Operators

These integrators are designed to be used with the MixedBilinearForm object to assemble square or rectangular linear operators.
These integrators are designed to be used with a `MixedBilinearForm` object to assemble square or rectangular linear operators.

| Class Name | Domain | Range | Coef. | Operator | Continuous Op. | Dimension |
|---------------------------------------|--------|--------|:-------:|------------------------------------------------|--------------------------------------|:----------:|
Expand Down Expand Up @@ -150,7 +150,7 @@ functions but others require one or the other.

### Square Operators

These integrators are designed to be used with the BilinearForm object
These integrators are designed to be used with a `BilinearForm` object
to assemble square linear operators.

| Class Name | Spaces | Coef. | Operator | Continuous Op. | Dimension |
Expand All @@ -161,7 +161,7 @@ to assemble square linear operators.

### Mixed Operators

These integrators are designed to be used with the MixedBilinearForm object to assemble square or rectangular linear operators.
These integrators are designed to be used with a `MixedBilinearForm` object to assemble square or rectangular linear operators.

| Class Name | Domain | Range | Coef. | Operator | Continuous Op. | Dimension |
|--------------------------------------|--------|--------|:-------:|----------------------------------------------------------|-----------------------------------------------|:----------:|
Expand Down Expand Up @@ -190,9 +190,9 @@ These integrators are designed to be used with the MixedBilinearForm object to a

| Class Name | Domain | Range | Coef. | Operator | Dimension | Notes |
|----------------------------------|--------|--------|-------|------------------------------------------------------------------------|:---------:|-------|
| VectorFEDivergenceIntegrator | RT | H1, L2 | S | $(\lambda\div\vec\{u}, v)$ | 2D, 3D | Alternate implementation of MixedScalarDivergenceIntegrator. |
| VectorFEWeakDivergenceIntegrator | ND | H1 | S | $(-\lambda\vec\{u},\grad v)$ | 2D, 3D | See MixedVectorWeakDivergenceIntegrator for a more general implementation. |
| VectorFECurlIntegrator | ND, RT | ND, RT | S | $(\lambda\curl\vec\{u},\vec\{v})$ or $(\lambda\vec\{u},\curl\vec\{v})$ | 3D | If the domain is ND then the Curl operator is returned, if the range is ND then the weak Curl is returned, otherwise a failure is encountered. See MixedVectorCurlIntegrator and MixedVectorWeakCurlIntegrator for more general implementations. |
| VectorFEDivergenceIntegrator | RT | H1, L2 | S | $(\lambda\div\vec\{u}, v)$ | 2D, 3D | Alternate implementation of `MixedScalarDivergenceIntegrator`. |
| VectorFEWeakDivergenceIntegrator | ND | H1 | S | $(-\lambda\vec\{u},\grad v)$ | 2D, 3D | See `MixedVectorWeakDivergenceIntegrator` for a more general implementation. |
| VectorFECurlIntegrator | ND, RT | ND, RT | S | $(\lambda\curl\vec\{u},\vec\{v})$ or $(\lambda\vec\{u},\curl\vec\{v})$ | 3D | If the domain is ND then the Curl operator is returned, if the range is ND then the weak Curl is returned, otherwise a failure is encountered. See `MixedVectorCurlIntegrator` and `MixedVectorWeakCurlIntegrator` for more general implementations. |

## Vector Field Operators

Expand Down Expand Up @@ -299,9 +299,9 @@ situations rather than needing to reimplement their functionality.

| Class Name | Description |
|---------------------|------------------------------------------------------------------------------------------------------------------------|
| TransposeIntegrator | Returns the transpose of the local matrix computed by another BilinearFormIntegrator |
| LumpedIntegrator | Returns a diagonal local matrix where each entry is the sum of the corresponding row of a local matrix computed by another BilinearFormIntegrator (only implemented for square matrices) |
| InverseIntegrator | Returns the inverse of the local matrix computed by another BilinearFormIntegrator which produces a square local matrix |
| TransposeIntegrator | Returns the transpose of the local matrix computed by another `BilinearFormIntegrator` |
| LumpedIntegrator | Returns a diagonal local matrix where each entry is the sum of the corresponding row of a local matrix computed by another `BilinearFormIntegrator` (only implemented for square matrices) |
| InverseIntegrator | Returns the inverse of the local matrix computed by another `BilinearFormIntegrator` which produces a square local matrix |
| SumIntegrator | Returns the sum of a series of integrators with compatible dimensions (only implemented for square matrices) |

## Weak Operators and Their Boundary Integrals
Expand Down