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A priori error estimates for the arbitrary Lagrangian Eulerian formulation with finite elements. (English) Zbl 0988.65082
The approximation by finite elements of a time-dependent advection-diffusion problem in a moving two-dimensional domain is considered. The author assumes that the motion of the boundary of the domain is given. This problem is discretized by linear finite elements in space and a modification of the implicit Euler scheme, based on the mid-point rule, in time. A priori error estimates optimal both in space and in time are derived, using slightly more regularity than for the case of non moving domains.

MSC:
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35K15 Initial value problems for second-order parabolic equations
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