Examples

Description

As part of the Platypus test suite, we solve a number of sample problems that may serve as a useful starting point for users to adapt:

Steady State Diffusion: Steady state diffusion problem for the temperature profile across a mug with fixed temperatures on two boundaries.
Transient Heat Transfer: Transient heat conduction problem with a boundary parameterized by a heat transfer coefficient that exchanges heat with a thermal reservoir.

Linear Elasticity: Solves a 3D linear elasticity problem for the deformation of a multi-material cantiliver beam. This example is based on MFEM Example 2.

Definite Maxwell: Solves a 3D electromagnetic diffusion problem for the electric field on a cube missing an octant, discretized using $var element = document.getElementById("moose-equation-083e7f22-dccd-46f9-844a-bbfaac9d134b");katex.render("H(\\mathrm{curl})", element, {displayMode:false,throwOnError:false});$ conforming Nédélec elements. This example is based on MFEM Example 3.
GradDiv: Solves a diffusion problem for a vector field on a cuboid domain, discretized using $var element = document.getElementById("moose-equation-09656dea-be5b-4b48-9b34-387ac9edc213");katex.render("H(\\mathrm{div})", element, {displayMode:false,throwOnError:false});$ conforming Raviart-Thomas elements. This example is based on MFEM Example 4 and is relevant for solving Maxwell's equations using potentials without the Coulomb gauge.