DESIGN AND CONVERGENCE OF AFEM IN H(DIV)
2007 ◽
Vol 17
(11)
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pp. 1849-1881
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Keyword(s):
We design an adaptive finite element method (AFEM) for mixed boundary value problems associated with the differential operator A-∇div in H(div, Ω). For A being a variable coefficient matrix with possible jump discontinuities, we provide a complete a posteriori error analysis which applies to both Raviart–Thomas ℝ𝕋n and Brezzi–Douglas–Marini 𝔹𝔻𝕄n elements of any order n in dimensions d = 2, 3. We prove a strict reduction of the total error between consecutive iterates, namely a contraction property for the sum of energy error and oscillation, the latter being solution-dependent. We present numerical experiments for ℝ𝕋n with n = 0, 1 and 𝔹𝔻𝕄1 which document the performance of AFEM and corroborate as well as extend the theory.
2017 ◽
Vol 327
◽
pp. 4-35
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2011 ◽
Vol 11
(2)
◽
pp. 107-128
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2020 ◽
Vol 369
◽
pp. 112574
◽
2016 ◽
pp. 449-453
2018 ◽
Vol 39
(4)
◽
pp. 1985-2015
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2021 ◽
Vol 381
◽
pp. 113015