Abstract
We introduce an abstract concept for decomposing spaces with respect to a substructuring of a bounded domain. In this setting we define weakly conforming finite element approximations of quadratic minimization problems. Within a saddle point approach the reduction to symmetric positive Schur complement systems on the skeleton is analyzed. Applications include weakly conforming variants of least squares and minimal residuals.
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References
F. Brezzi, M. Fortin, Mixed and Hybrid Finite Element Methods (Springer, New York, 1991)
T. Bui-Thanh, L.F. Demkowicz, O. Ghattas, A unified discontinuous Petrov–Galerkin method and its analysis for Friedrich systems. SIAM J. Numer. Anal. 51 (4), 1933–1958 (2013)
C. Carstensen, L.F. Demkowicz, J. Gopalakrishnan, Breaking spaces and forms for the DPG method and applications including Maxwell equations, Technical report, 2015, ICES Report 15-18
L.F. Demkowicz, J. Gopalakrishnan, An overview of the discontinuous Petrov–Galerkin method, in Recent Developments in Discontinuous Galerkin Finite Element Methods for Partial Differential Equations (Springer, Springer International Publishing Switzerland, 2014), pp. 149–180
A. Ern, J.-L. Guermond, G. Caplain, An intrinsic criterion for the bijectivity of Hilbert operators related to Friedrich systems. Commun. Partial Differ. Equ. 32 (2), 317–341 (2007)
J. Gopalakrishnan, W. Qiu, An analysis of the practical DPG method. Math. Comput. 83 (286), 537–552 (2014)
C. Wieners, B. Wohlmuth, Robust operator estimates and the application to substructuring methods for first-order systems. ESAIM: M 2AN 48, 161–175 (2014)
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Wieners, C. (2016). The Skeleton Reduction for Finite Element Substructuring Methods. In: Karasözen, B., Manguoğlu, M., Tezer-Sezgin, M., Göktepe, S., Uğur, Ö. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2015. Lecture Notes in Computational Science and Engineering, vol 112. Springer, Cham. https://doi.org/10.1007/978-3-319-39929-4_14
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DOI: https://doi.org/10.1007/978-3-319-39929-4_14
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