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- W989543777 abstract "Publisher Summary This chapter discusses application to primitive and wave equations. The order of consistency is a direct measure of the speed at which a model converges to the exact solution as the elements become finer. As such, consistency unveils the behavior of the numerical solution, in the limit, where the grid spacing is reduced to zero. Here, the analysis is restricted to the spatial semi-discretization. Often, one may establish the consistency of an approximation by proving that the local truncation error goes to zero in the limit as the grid size is reduced to zero. When the solution is well-behaved, the natural tool for such an analysis is the Taylor series expansion. Then, the approximation is expanded around a point. This leads to an expression containing the exact differential equation plus some error terms. Because, the order of consistency represents the rate at which the approximate solution approaches the exact solution as the mesh is refined, it is desirable to build models with a high order of consistency. For finite element method (FEM), a definition of consistency in a global sense is more appropriate." @default.
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- W989543777 date "1988-01-01" @default.
- W989543777 modified "2023-09-27" @default.
- W989543777 title "A Consistency Analysis of the FEM: Application to Primitive and Wave Equations" @default.
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- W989543777 doi "https://doi.org/10.1016/s0167-5648(08)70342-3" @default.
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