Model Problems
The following model problems are available and are dispatched via the following types.
ExtendableASGFEM.PoissonProblemPrimal — Typeabstract type PoissonProblemPrimal <: ExtendableASGFEM.AbstractModelProblemPoisson problem with linear stochastic coefficient $a$ that seeks $u$ such that
$-\mathrm{div}(a(y,x) \nabla u(y,x)) = f(x) \quad \text{for } (y,x) \in \Gamma \times D$
ExtendableASGFEM.LogTransformedPoissonProblemPrimal — Typeabstract type LogTransformedPoissonProblemPrimal <: ExtendableASGFEM.AbstractModelProblemPoisson problem with exponential stochastic coefficient $e^a$ that seeks $u$ such that
$-\mathrm{div}(e^a(y,x) \nabla u(y,x)) = f(x) \quad \text{for } (y,x) \in \Gamma \times D$
The stochastic Galerkin FEM solves the equivalent transformed problem
$-\mathrm{div}(\nabla u(y,x)) - \nabla a(y,x) \cdot \nabla u(y,x) = e^{-a(y,x)} f(x) \quad \text{for } (y,x) \in \Gamma \times D$
ExtendableASGFEM.LogTransformedPoissonProblemDual — Typeabstract type LogTransformedPoissonProblemDual <: ExtendableASGFEM.AbstractModelProblemDual log-transformed formulation of the Poisson problem with exponential stochastic coefficient (WIP).