SIAM Journal on Numerical Analysis · 1989 · 10 citations · 3 references
EngineeringComputational EngineeringPhysicsComputational Heat TransferComputational PhysicsHeat TransferBoundary ConditionsHeat Transfer AnalysisIterative SolversMoving Boundary ProblemsNumerical AlgorithmsNumerical Methods For Differential EquationsError BoundsHeat EquationNumerical DiscretizationOne-dimensional Heat TransferPartial Differential Equation SolversTime DiscretizationTime Discretization Error Analysis
A discretization of the one-dimensional heat equation in a time-dependent domain is considered, with particular emphasis on a generalization of the Crank–Nicholson scheme for the discretization with respect to time. Application to a one-dimensional Stefan problem is given, with an iterative algorithm to follow the moving boundary. Numerical results agree well with the theoretical error bounds.
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