Implicit two-derivative deferred correction time discretization for the discontinuous Galerkin method

Functional‐preserving predictor‐corrector multiderivative schemes

“…For considerations regarding Newton efficiency, we refer the reader to ref. [14]. In all the numerical results, ‘error’ is defined as the Euclidean error of the discrete solution at the final time $$T_{end}$$.…”

“…[3], the multiderivative paradigm has only been rediscovered rather recently; for some examples see refs. [4][5][6][7][8][9] and the references therein.…”

“…[12,13]. HBPC has shown favorable behavior for the solution of compressible flow equations [9,14,15]. While linear stability of HBPC has been tackled in ref.…”

“…[12, 13]. HBPC has shown favorable behavior for the solution of compressible flow equations [9, 14, 15].…”

Semi-implicit high resolution numerical scheme for conservation laws

“…We mention explicit methods based on Taylor series expansions like the Lax-Wendroff procedure [29,39,9,10], a local time-space DG discretization [12,20], and two-, or even multi-derivative implicit schemes [18], see also a review paper [30]. Concerning the methods based on Taylor series, several authors have recognized that it can be advantageous to discretize each replaced term in the Taylor expansion with different spatial discretizations [29,30,36,24,9,38]. A natural question arises if such an approach can be used to simplify the algebraic equations resulting from implicit or implicit-explicit time discretization of hyperbolic problems.…”