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NUMERICAL HOMOGENIZ...
NUMERICAL HOMOGENIZATION OF H(CURL)-PROBLEMS
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- Gallistl, Dietmar (author)
- Univ Twente, Fac Elect Engn Math & Comp Sci, POB 217, NL-7500 AE Enschede, Netherlands.
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- Henning, Patrick, 1983- (author)
- KTH,Numerisk analys, NA
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- Verfuerth, Barbara (author)
- Westfalische Wilhelms Univ Munster, Appl Math, D-48149 Munster, Germany.
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Univ Twente, Fac Elect Engn Math & Comp Sci, POB 217, NL-7500 AE Enschede, Netherlands Numerisk analys, NA (creator_code:org_t)
- SIAM PUBLICATIONS, 2018
- 2018
- English.
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In: SIAM Journal on Numerical Analysis. - : SIAM PUBLICATIONS. - 0036-1429 .- 1095-7170. ; 56:3, s. 1570-1596
- Related links:
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https://urn.kb.se/re...
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https://doi.org/10.1...
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Abstract
Subject headings
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- If an elliptic differential operator associated with an H (curl)- problem involves rough (rapidly varying) coefficients, then solutions to the corresponding H (curl)- problem admit typically very low regularity, which leads to arbitrarily bad convergence rates for conventional numerical schemes. The goal of this paper is to show that the missing regularity can be compensated through a corrector operator. More precisely, we consider the lowest-order Nedelec finite element space and show the existence of a linear corrector operator with four central properties: it is computable, H (curl)- stable, and quasi-local and allows for a correction of coarse finite element functions so that first-order estimates (in terms of the coarse mesh size) in the H (curl) norm are obtained provided the right-hand side belongs to H (div). With these four properties, a practical application is to construct generalized finite element spaces which can be straightforwardly used in a Galerkin method. In particular, this characterizes a homogenized solution and a first-order corrector, including corresponding quantitative error estimates without the requirement of scale separation. The constructed generalized finite element method falls into the class of localized orthogonal decomposition methods, which have not been studied for H (curl)- problems so far.
Subject headings
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
Keyword
- multiscale method
- wave propagation
- Maxwell's equations
- finite element method
- a priori error estimates
Publication and Content Type
- ref (subject category)
- art (subject category)
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