The discontinuous control-volume finite-element method is applied to the one-dimensional advection-diffusion equation and validated on relevant test cases. The technique merges the features of the classical finite-volume method, as robustness and local conservation properties [1], with those of the discontinuous Galerkin finite-element method, known for the capability of handling large gradients or discontinuities with high accuracy [2]. On the other hand, most finite-volume methods attain relatively low orders of spatial accuracy and resolution characteristics, particularly on unstructured meshes. To achieve high-order accuracy, the proposed technique adopts polynomial shape functions of any degree as in spectral finite-element methods [3]. In many applications high resolution is not needed in the whole domain, which results also in a loss of computational resources. We thus apply an automatic p-refinement technique which adapts the polynomial order at element level, according to the local behavior of the computed solution. Element-wise p-adaption can be easily achieved with discontinuous Galerkin methods, where the inter-element continuity is imposed in weak form.

Development and application of high-order discontinuous CVFEM algorithms

STIPCICH, GORAN;PILLER, MARZIO;ZOVATTO, LUIGINO
2010

Abstract

The discontinuous control-volume finite-element method is applied to the one-dimensional advection-diffusion equation and validated on relevant test cases. The technique merges the features of the classical finite-volume method, as robustness and local conservation properties [1], with those of the discontinuous Galerkin finite-element method, known for the capability of handling large gradients or discontinuities with high accuracy [2]. On the other hand, most finite-volume methods attain relatively low orders of spatial accuracy and resolution characteristics, particularly on unstructured meshes. To achieve high-order accuracy, the proposed technique adopts polynomial shape functions of any degree as in spectral finite-element methods [3]. In many applications high resolution is not needed in the whole domain, which results also in a loss of computational resources. We thus apply an automatic p-refinement technique which adapts the polynomial order at element level, according to the local behavior of the computed solution. Element-wise p-adaption can be easily achieved with discontinuous Galerkin methods, where the inter-element continuity is imposed in weak form.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11368/2299822
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact