Heat Equation

\[\frac{\partial u}{\partial t} -\Delta u = f\]

Input file:

mesh:
  type: RectangleMesh
  nx: 2
  ny: 2

problem:
  type: HeatEquationProblem
  start_time: 0
  end_time: 0.1
  dt: 0.001

ics:
  all:
    type: ConstantInitialCondition
    value: [ 300 ]

bcs:
  left:
    type: DirichletBC
    boundary: [ 'left' ]
    value: [ '310' ]
  right:
    type: DirichletBC
    boundary: [ 'right' ]
    value: [ '300' ]

output:
  vtk:
    type: VTKOutput
    file: 'out'