- Title
- The Hessian discretisation method for fourth order linear elliptic equations
- Creator
- Droniou, Jérôme; Lamichhane, Bishnu P.; Shylaja, Devika
- Relation
- Journal of Scientific Computing Vol. 78, Issue 3, p. 1405-1437
- Publisher Link
- http://dx.doi.org/10.1007/s10915-018-0814-7
- Publisher
- Springer
- Resource Type
- journal article
- Date
- 2019
- Description
- 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 ℙ₁ finite element space and gradient recovery operators. Results of numerical experiments are presented for this novel scheme and for a finite volume scheme.
- Subject
- fourth order elliptic equations; numerical schemes; error estimates; Hessian discretisation method; Hessian schemes; finite element method; finite volume method; gradient recovery method
- Identifier
- http://hdl.handle.net/1959.13/1417873
- Identifier
- uon:37270
- Identifier
- ISSN:0885-7474
- Rights
- This is a post-peer-review, pre-copyedit version of an article published in Journal of Scientific Computing. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10915-018-0814-7.
- Language
- eng
- Full Text
- Reviewed
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