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• W1644103674 abstract "Mesh adaption procedures for finite element approximation allows one to adapt the resolution, by local refinement in the regions of strong variation of the function of interest. This procedure plays a key role in numerous applications of scientific computing. The use of anisotropic triangles allows to improve the efficiency of the procedure by introducing long and thin triangles that fit in particular the directions of the possible curves of discontinuity. Given a norm X of interest and a function f to be approximated, we formulate the problem of optimal mesh adaptation, as minimizing the approximation error over all (possibly anisotropic) triangulations of prescribed cardinality. We address the four following questions related to this problem: I. How does the approximation error behave in the asymptotic regime when the number of triangles N tends to infinity, when f is a smooth function ? II. Which classes of functions govern the rate of decay of the approximation error as N grows, and are in that sense naturally tied to the problem of optimal mesh adaptation? III. Could this optimization problem, which is posed on triangulations of a given cardinality N, be replaced by an equivalent more tractable problem posed on a continuous object? IV. Is it possible to produce a near-optimal sequence of triangulations using a hierarchical refinement procedure?" @default.
• W1644103674 created "2016-06-24" @default.
• W1644103674 creator A5029194666 @default.
• W1644103674 date "2010-12-06" @default.
• W1644103674 modified "2023-09-27" @default.
• W1644103674 title "Adaptive and anisotropic finite element approximation: Theory and algorithms" @default.
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• W1644103674 hasPublicationYear "2010" @default.
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