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The Hessian discretisation method for fourth order linear elliptic equations. (arXiv:1803.06985v2 [math.NA] UPDATED)
来源于:arXiv
In this paper, we propose a unified framework, the Hessian discretisation
method (HDM), which is based on four discrete elements (called altogether a
Hessian discretisation) and a few intrinsic indicators of accuracy, independent
of the considered model. An error estimate is obtained, using only these
intrinsic indicators, when the HDM framework is applied to linear fourth order
problems. It is shown that HDM encompasses a large number of numerical methods
for fourth order elliptic problems: finite element methods (conforming and
non-conforming) as well as finite volume methods. We also use the HDM to design
a novel method, based on conforming $\mathbb{P}_1$ finite element space and
gradient recovery operators. Results of numerical experiments are presented for
this novel scheme and for a finite volume scheme. 查看全文>>