Parker, Charles; Süli, Endre Stable lifting of polynomial traces on triangles. (English) Zbl 07821070 SIAM J. Numer. Anal. 62, No. 2, 692-717 (2024). MSC: 46E35 65N30 PDFBibTeX XMLCite \textit{C. Parker} and \textit{E. Süli}, SIAM J. Numer. Anal. 62, No. 2, 692--717 (2024; Zbl 07821070) Full Text: DOI arXiv
Falk, Richard S.; Winther, Ragnar The bubble transform and the de Rham complex. (English) Zbl 07808383 Found. Comput. Math. 24, No. 1, 99-147 (2024). MSC: 65N30 52-08 58A12 58A10 65N50 65N55 PDFBibTeX XMLCite \textit{R. S. Falk} and \textit{R. Winther}, Found. Comput. Math. 24, No. 1, 99--147 (2024; Zbl 07808383) Full Text: DOI arXiv
Falk, Richard S.; Winther, Ragnar Construction of polynomial preserving cochain extensions by blending. (English) Zbl 1512.65266 Math. Comput. 92, No. 342, 1575-1594 (2023). MSC: 65N30 65D17 65D18 58A12 58A10 PDFBibTeX XMLCite \textit{R. S. Falk} and \textit{R. Winther}, Math. Comput. 92, No. 342, 1575--1594 (2023; Zbl 1512.65266) Full Text: DOI arXiv
Chaumont-Frelet, T.; Ern, A.; Vohralík, M. Stable broken \(\boldsymbol{H}(\mathbf{curl})\) polynomial extensions and \(p\)-robust a posteriori error estimates by broken patchwise equilibration for the curl-curl problem. (English) Zbl 1479.65027 Math. Comput. 91, No. 333, 37-74 (2022). MSC: 65N30 78M10 65N15 46E35 PDFBibTeX XMLCite \textit{T. Chaumont-Frelet} et al., Math. Comput. 91, No. 333, 37--74 (2022; Zbl 1479.65027) Full Text: DOI arXiv
Ye, Xiu; Zhang, Shangyou A \(P_{k + 2}\) polynomial lifting operator on polygons and polyhedrons. (English) Zbl 1468.65208 Appl. Math. Lett. 116, Article ID 107033, 6 p. (2021). MSC: 65N30 35J05 PDFBibTeX XMLCite \textit{X. Ye} and \textit{S. Zhang}, Appl. Math. Lett. 116, Article ID 107033, 6 p. (2021; Zbl 1468.65208) Full Text: DOI arXiv
Chaumont-Frelet, Théophile; Ern, Alexandre; Vohralík, Martin Polynomial-degree-robust \(\boldsymbol H(\mathbf{curl})\)-stability of discrete minimization in a tetrahedron. (English. French summary) Zbl 1456.65156 C. R., Math., Acad. Sci. Paris 358, No. 9-10, 1101-1110 (2020). MSC: 65N30 65K10 65N15 35J05 78M10 35Q60 46E35 PDFBibTeX XMLCite \textit{T. Chaumont-Frelet} et al., C. R., Math., Acad. Sci. Paris 358, No. 9--10, 1101--1110 (2020; Zbl 1456.65156) Full Text: DOI arXiv
Demkowicz, Leszek; Gopalakrishnan, Jay; Keith, Brendan The DPG-star method. (English) Zbl 1447.65133 Comput. Math. Appl. 79, No. 11, 3092-3116 (2020). MSC: 65N30 65F20 65N12 65N15 35B45 35N25 PDFBibTeX XMLCite \textit{L. Demkowicz} et al., Comput. Math. Appl. 79, No. 11, 3092--3116 (2020; Zbl 1447.65133) Full Text: DOI arXiv
Ainsworth, Mark; Parker, Charles \(H^2\)-stable polynomial liftings on triangles. (English) Zbl 1460.46020 SIAM J. Numer. Anal. 58, No. 3, 1867-1892 (2020). MSC: 46E35 65N55 PDFBibTeX XMLCite \textit{M. Ainsworth} and \textit{C. Parker}, SIAM J. Numer. Anal. 58, No. 3, 1867--1892 (2020; Zbl 1460.46020) Full Text: DOI
Ern, Alexandre; Vohralík, Martin Stable broken \(H^1\) and \(H(\operatorname{div})\) polynomial extensions for polynomial-degree-robust potential and flux reconstruction in three space dimensions. (English) Zbl 1434.65253 Math. Comput. 89, No. 322, 551-594 (2020). MSC: 65N30 65N15 76M10 46E35 PDFBibTeX XMLCite \textit{A. Ern} and \textit{M. Vohralík}, Math. Comput. 89, No. 322, 551--594 (2020; Zbl 1434.65253) Full Text: DOI arXiv
Melenk, J. M.; Rojik, C. On commuting \(p\)-version projection-based interpolation on tetrahedra. (English) Zbl 1426.65181 Math. Comput. 89, No. 321, 45-87 (2020). MSC: 65N30 65N35 65N12 78M10 PDFBibTeX XMLCite \textit{J. M. Melenk} and \textit{C. Rojik}, Math. Comput. 89, No. 321, 45--87 (2020; Zbl 1426.65181) Full Text: DOI arXiv
Canuto, Claudio; Nochetto, Ricardo H.; Stevenson, Rob P.; Verani, Marco A saturation property for the spectral-Galerkin approximation of a Dirichlet problem in a square. (English) Zbl 1426.65187 ESAIM, Math. Model. Numer. Anal. 53, No. 3, 987-1003 (2019). Reviewer: Marius Ghergu (Dublin) MSC: 65N35 65N30 65N50 65N55 65N15 35J05 PDFBibTeX XMLCite \textit{C. Canuto} et al., ESAIM, Math. Model. Numer. Anal. 53, No. 3, 987--1003 (2019; Zbl 1426.65187) Full Text: DOI arXiv
Cancès, Eric; Dusson, Geneviève; Maday, Yvon; Stamm, Benjamin; Vohralík, Martin Guaranteed and robust a posteriori bounds for Laplace eigenvalues and eigenvectors: a unified framework. (English) Zbl 1402.65137 Numer. Math. 140, No. 4, 1033-1079 (2018). MSC: 65N15 35P15 65N25 65N30 65N50 PDFBibTeX XMLCite \textit{E. Cancès} et al., Numer. Math. 140, No. 4, 1033--1079 (2018; Zbl 1402.65137) Full Text: DOI Link
Barker, A. T.; Dobrev, V.; Gopalakrishnan, J.; Kolev, T. A scalable preconditioner for a primal discontinuous Petrov-Galerkin method. (English) Zbl 1448.65213 SIAM J. Sci. Comput. 40, No. 2, A1187-A1203 (2018). MSC: 65N30 65N55 65F10 65F08 PDFBibTeX XMLCite \textit{A. T. Barker} et al., SIAM J. Sci. Comput. 40, No. 2, A1187--A1203 (2018; Zbl 1448.65213) Full Text: DOI arXiv
Fuentes, Federico; Demkowicz, Leszek; Wilder, Aleta Using a DPG method to validate DMA experimental calibration of viscoelastic materials. (English) Zbl 1439.74080 Comput. Methods Appl. Mech. Eng. 325, 748-765 (2017). MSC: 74D05 74S05 65M60 PDFBibTeX XMLCite \textit{F. Fuentes} et al., Comput. Methods Appl. Mech. Eng. 325, 748--765 (2017; Zbl 1439.74080) Full Text: DOI arXiv
Ern, Alexandre; Smears, Iain; Vohralík, Martin Discrete \(p\)-robust \(\boldsymbol H(\mathrm{div})\)-liftings and a posteriori estimates for elliptic problems with \(H^{-1}\) source terms. (English) Zbl 1378.65173 Calcolo 54, No. 3, 1009-1025 (2017). Reviewer: Seenith Sivasundaram (Daytona Beach) MSC: 65N15 35J25 PDFBibTeX XMLCite \textit{A. Ern} et al., Calcolo 54, No. 3, 1009--1025 (2017; Zbl 1378.65173) Full Text: DOI arXiv
Canuto, Claudio; Nochetto, Ricardo H.; Stevenson, Rob; Verani, Marco On \(p\)-robust saturation for \(hp\)-AFEM. (English) Zbl 1373.65082 Comput. Math. Appl. 73, No. 9, 2004-2022 (2017). MSC: 65N30 65N15 65N50 35J05 PDFBibTeX XMLCite \textit{C. Canuto} et al., Comput. Math. Appl. 73, No. 9, 2004--2022 (2017; Zbl 1373.65082) Full Text: DOI arXiv
Chen, Huangxin; Qiu, Weifeng A first order system least squares method for the Helmholtz equation. (English) Zbl 1347.65174 J. Comput. Appl. Math. 309, 145-162 (2017). MSC: 65N30 65L12 PDFBibTeX XMLCite \textit{H. Chen} and \textit{W. Qiu}, J. Comput. Appl. Math. 309, 145--162 (2017; Zbl 1347.65174) Full Text: DOI arXiv
Carstensen, C.; Demkowicz, L.; Gopalakrishnan, J. Breaking spaces and forms for the DPG method and applications including Maxwell equations. (English) Zbl 1359.65249 Comput. Math. Appl. 72, No. 3, 494-522 (2016). MSC: 65N30 65N12 78A25 78M10 PDFBibTeX XMLCite \textit{C. Carstensen} et al., Comput. Math. Appl. 72, No. 3, 494--522 (2016; Zbl 1359.65249) Full Text: DOI arXiv
Dolejší, Vít; Ern, Alexandre; Vohralík, Martin \(hp\)-adaptation driven by polynomial-degree-robust a posteriori error estimates for elliptic problems. (English) Zbl 1351.65082 SIAM J. Sci. Comput. 38, No. 5, A3220-A3246 (2016). MSC: 65N15 35J25 35J05 65N30 65N12 65N50 PDFBibTeX XMLCite \textit{V. Dolejší} et al., SIAM J. Sci. Comput. 38, No. 5, A3220--A3246 (2016; Zbl 1351.65082) Full Text: DOI
Falk, Richard S.; Winther, Ragnar The bubble transform: a new tool for analysis of finite element methods. (English) Zbl 1337.65152 Found. Comput. Math. 16, No. 1, 297-328 (2016). Reviewer: Pavol Chocholatý (Bratislava) MSC: 65N30 PDFBibTeX XMLCite \textit{R. S. Falk} and \textit{R. Winther}, Found. Comput. Math. 16, No. 1, 297--328 (2016; Zbl 1337.65152) Full Text: DOI arXiv
Ern, Alexandre; Vohralík, Martin Polynomial-degree-robust a posteriori estimates in a unified setting for conforming, nonconforming, discontinuous Galerkin, and mixed discretizations. (English) Zbl 1312.76026 SIAM J. Numer. Anal. 53, No. 2, 1058-1081 (2015). MSC: 76M10 65N15 65N30 PDFBibTeX XMLCite \textit{A. Ern} and \textit{M. Vohralík}, SIAM J. Numer. Anal. 53, No. 2, 1058--1081 (2015; Zbl 1312.76026) Full Text: DOI
Gopalakrishnan, J.; Qiu, W. An analysis of the practical DPG method. (English) Zbl 1282.65154 Math. Comput. 83, No. 286, 537-552 (2014). Reviewer: Tomas Vejchodsky (Praha) MSC: 65N30 65N12 65N15 35J05 74B05 74S05 PDFBibTeX XMLCite \textit{J. Gopalakrishnan} and \textit{W. Qiu}, Math. Comput. 83, No. 286, 537--552 (2014; Zbl 1282.65154) Full Text: DOI arXiv
Bramwell, Jamie; Demkowicz, Leszek; Gopalakrishnan, Jay; Qiu, Weifeng A locking-free \(hp\) DPG method for linear elasticity with symmetric stresses. (English) Zbl 1283.74094 Numer. Math. 122, No. 4, 671-707 (2012). MSC: 74S05 74B05 PDFBibTeX XMLCite \textit{J. Bramwell} et al., Numer. Math. 122, No. 4, 671--707 (2012; Zbl 1283.74094) Full Text: DOI arXiv
Gopalakrishnan, Jay; Qiu, Weifeng Partial expansion of a Lipschitz domain and some applications. (English) Zbl 1255.65149 Front. Math. China 7, No. 2, 249-272 (2012). Reviewer: Rémi Vaillancourt (Ottawa) MSC: 65L60 65N30 46E35 52B10 26A16 PDFBibTeX XMLCite \textit{J. Gopalakrishnan} and \textit{W. Qiu}, Front. Math. China 7, No. 2, 249--272 (2012; Zbl 1255.65149) Full Text: DOI arXiv