# `pymor.analyticalproblems.elliptic`¶

## Module Contents¶

### Classes¶

 `StationaryProblem` Linear elliptic problem description.

Linear elliptic problem description.

The problem consists in solving

```- ∇ ⋅ [d(x, μ) ∇ u(x, μ)] + ∇ ⋅ [f_l(x, μ)u(x, μ)]
+ ∇ ⋅ f_n(u(x, μ), μ) + c_l(x, μ) + c_n(u(x, μ), μ) = g(x, μ)
```

for u.

Parameters

domain

A `DomainDescription` of the domain the problem is posed on.

rhs

The `Function` g. `rhs.dim_domain` has to agree with the dimension of `domain`, whereas `rhs.shape_range` has to be `()`.

diffusion

The `Function` d with `shape_range` of either `()` or `(dim domain, dim domain)`.

The `Function` f_l, only depending on x, with `shape_range` of `(dim domain,)`.

The `Function` f_n, only depending on u, with `shape_range` of `(dim domain,)`.

The derivative of f_n, only depending on u, with respect to u.

reaction

The `Function` c_l, only depending on x, with `shape_range` of `()`.

nonlinear_reaction

The `Function` c_n, only depending on u, with `shape_range` of `()`.

nonlinear_reaction_derivative

The derivative of the `Function` c_n, only depending on u, with `shape_range` of `()`.

dirichlet_data

`Function` providing the Dirichlet boundary values.

neumann_data

`Function` providing the Neumann boundary values.

robin_data

Tuple of two `Functions` providing the Robin parameter and boundary values.

outputs

Tuple of additional output functionals to assemble. Each value must be a tuple of the form `(functional_type, data)` where `functional_type` is a string defining the type of functional to assemble and `data` is a `Function` holding the corresponding coefficient function. Currently implemented `functional_types` are:

l2

Evaluate the l2-product with the given data function.

l2_boundary

Evaluate the l2-product with the given data function on the boundary.

parameter_ranges

Ranges of interest for the `Parameters` of the problem.

name

Name of the problem.

domain[source]
rhs[source]
diffusion[source]