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A new strategy for finite element computations involving moving boundaries and interfaces — The deforming-spatial-domain/space-time procedure. I: The concept and the preliminary numerical tests. (English) Zbl 0745.76044
Summary: A new strategy based on the stabilized space-time finite element formulation is proposed for computations involving moving boundaries and interfaces. In the deforming-spatial-domain/ space-time procedure the variational formulation of a problem is written over its space-time domain, and therefore the deformation of the spatial domain with respect to time is taken into account automatically. Because the space-time mesh is generated over the space-time domain of the problem, within each time step, the boundary (or interface) nodes move with the boundary (or interface). Whether the motion of the boundary is specified or not, the strategy is nearly the same. If the motion of the boundary is unknown, then the boundary nodes move as defined by the other unknowns at the boundary (such as the velocity or the displacement). At the end of each time step a new spatial mesh covers the new spatial domain. For computational feasibility, the finite element interpolation functions are chosen to be discontinuous in time, and the fully discretized equations are solved one space-time slab at a time.

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
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