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High‐order finite volume schemes based on defect corrections
Author(s) -
Filimon A.,
Dumbser M.,
Munz C.D.
Publication year - 2013
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201200007
Subject(s) - stencil , discretization , finite volume method , a priori and a posteriori , iterated function , solver , mathematics , order (exchange) , scheme (mathematics) , order of accuracy , polynomial , algorithm , mathematical optimization , computer science , mathematical analysis , numerical analysis , computational science , physics , philosophy , epistemology , finance , numerical stability , mechanics , economics
For the approximation of steady state solutions, we propose an iterated defect correction approach to achieve higher‐order accuracy. The procedure starts with the steady state solution of a low‐order scheme, in general a second order one. The higher‐order reconstruction step is applied a posteriori to estimate the local discretization error of the lower‐order finite volume scheme. The defect is then used to iteratively shift the basic lower‐order scheme to the desired higher‐order accuracy given by the polynomial reconstruction. Hence, instead of solving the high‐order discrete equations the low‐order basic scheme is solved several times. This avoids that the high‐order reconstruction with a large stencil has to be implemented into an existing basic solver and can be seen as a non‐intrusive approach to higher‐order accuracy.