ADER High-Order Methods

Eleuterio F. Toro ()
Additional contact information
Eleuterio F. Toro: University of Trento, DICAM

Chapter Chapter 14 in Computational Algorithms for Shallow Water Equations, 2024, pp 317-351 from Springer

Abstract: Abstract This chapter is concerned with advanced, numerical methods for evolutionary partial differential equations, following the ADER framework. The methodology is an unlimited-order, non-linear fully discrete one-step extension of Godunov’s method that operates in the finite volume and discontinuous Galerkin finite element frameworks. The approach is applicable to multidimensional systems in conservative and non-conservative forms, on structured and unstructured meshes. The building block of ADER is the generalised Riemann problem $$GRP_{m}$$ G R P m , admitting stiff and non-stiff source terms, with initial data consisting of reconstruction polynomials of arbitrary degree m. The resulting ADER schemes are of order $$m+1$$ m + 1 in both space and time. Here we review some key aspects of the methodology and give appropriate references. The presentation is general, so as to include any system of hyperbolic balance laws and extensions, but we also identify specific applications to the shallow water equations of interest in this book. The chapter is concluded with two examples that highlight the key point of very high-order methods; that is, for small errors high-order ADER methods are orders-of-magnitude more efficient than low-order methods.

Date: 2024
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-61395-1_14

Ordering information: This item can be ordered from
http://www.springer.com/9783031613951

DOI: 10.1007/978-3-031-61395-1_14

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().