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high_order_time_integration.i
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high_order_time_integration.i
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[Mesh]
type = GeneratedMesh
dim = 2
nx = 10
ny = 10
[]
[Variables]
[./u]
[../]
[./v]
[../]
[]
[AuxVariables]
[./exact_solution]
[../]
[]
[Kernels]
[./diff]
type = CoefDiffusion
variable = u
coef = 0.1
[../]
[./time]
type = TimeDerivative
variable = u
[../]
[]
[NodalKernels]
[./td]
type = TimeDerivativeNodalKernel
variable = v
[../]
[./f]
type = UserForcingFunctionNodalKernel
variable = v
function = t*t*t+4
[../]
[]
[AuxKernels]
[./exact]
type = FunctionAux
variable = exact_solution
function = exact_solution_function
[../]
[]
[BCs]
[./left]
type = DirichletBC
variable = u
boundary = left
value = 0
[../]
[./right]
type = DirichletBC
variable = u
boundary = right
value = 1
[../]
[]
[Functions]
[./exact_solution_function]
type = ParsedFunction
value = (1.0/4.0)*(16*t+t*t*t*t)
[../]
[]
[Postprocessors]
[./error]
type = NodalL2Error
variable = v
function = exact_solution_function
[../]
[]
[Executioner]
# Preconditioned JFNK (default)
type = Transient
end_time = 20
dt = 1
solve_type = PJFNK
petsc_options_iname = '-pc_type -pc_hypre_type'
petsc_options_value = 'hypre boomeramg'
scheme = 'crank-nicolson'
[]
[Outputs]
exodus = true
csv = true
[]