Duczek, S.; Saputra, A. A.; Gravenkamp, Hauke High order transition elements: the \(x\boldsymbol{N}y\)-element concept. I: Statics. (English) Zbl 1439.74408 Comput. Methods Appl. Mech. Eng. 362, Article ID 112833, 50 p. (2020). MSC: 74S05 65N30 PDF BibTeX XML Cite \textit{S. Duczek} et al., Comput. Methods Appl. Mech. Eng. 362, Article ID 112833, 50 p. (2020; Zbl 1439.74408) Full Text: DOI arXiv
Maday, Yvon \(h-P\) finite element approximation for full-potential electronic structure calculations. (English) Zbl 1318.65070 Ciarlet, Philippe G. (ed.) et al., Partial differential equations. Theory, control and approximation. In honor of the scientific heritage of Jacques-Louis Lions. Selected papers based on the presentations at the international conference on partial differential equations: theory, control and approximation, Shanghai, China, May 28 – June 1, 2012. Berlin: Springer (ISBN 978-3-642-41400-8/hbk; 978-3-642-41401-5/ebook). 349-377 (2014). MSC: 65N25 35Q40 65N30 35P30 81Q05 PDF BibTeX XML Cite \textit{Y. Maday}, in: Partial differential equations. Theory, control and approximation. In honor of the scientific heritage of Jacques-Louis Lions. Selected papers based on the presentations at the international conference on partial differential equations: theory, control and approximation, Shanghai, China, May 28 -- June 1, 2012. Berlin: Springer. 349--377 (2014; Zbl 1318.65070) Full Text: DOI
Maday, Yvon \({h-P}\) finite element approximation for full-potential electronic structure calculations. (English) Zbl 1302.65255 Chin. Ann. Math., Ser. B 35, No. 1, 1-24 (2014). MSC: 65N30 65N25 65T99 35P30 35Q40 81Q05 PDF BibTeX XML Cite \textit{Y. Maday}, Chin. Ann. Math., Ser. B 35, No. 1, 1--24 (2014; Zbl 1302.65255) Full Text: DOI
Guo, Benqi; Babuška, Ivo Direct and inverse approximation theorems for the \(p\)-version of the finite element method in the framework of weighted Besov spaces. III: Inverse approximation theorems. (English) Zbl 1382.65399 J. Approx. Theory 173, 122-157 (2013). MSC: 65N30 46E35 65N12 65N15 35J25 PDF BibTeX XML Cite \textit{B. Guo} and \textit{I. Babuška}, J. Approx. Theory 173, 122--157 (2013; Zbl 1382.65399) Full Text: DOI
Schillinger, Dominik; Ruess, Martin; Zander, Nils; Bazilevs, Yuri; Düster, Alexander; Rank, Ernst Small and large deformation analysis with the \(p\)- and B-spline versions of the finite cell method. (English) Zbl 1398.74401 Comput. Mech. 50, No. 4, 445-478 (2012). MSC: 74S05 65N30 74S30 76M10 74B20 42C40 PDF BibTeX XML Cite \textit{D. Schillinger} et al., Comput. Mech. 50, No. 4, 445--478 (2012; Zbl 1398.74401) Full Text: DOI
Goudenège, Ludovic; Martin, Daniel; Vial, Grégory High order finite element calculations for the Cahn-Hilliard equation. (English) Zbl 1257.82004 J. Sci. Comput. 52, No. 2, 294-321 (2012). MSC: 82-08 82C80 65M60 35Q82 PDF BibTeX XML Cite \textit{L. Goudenège} et al., J. Sci. Comput. 52, No. 2, 294--321 (2012; Zbl 1257.82004) Full Text: DOI arXiv
Yi, Lijun; Guo, Benqi Superconvergence of the \(h\)-\(p\) version of the finite element method in one dimension. (English) Zbl 1175.65090 J. Comput. Appl. Math. 233, No. 2, 150-164 (2009). Reviewer: Pavol Chocholatý (Bratislava) MSC: 65L20 65L60 65N30 65N15 PDF BibTeX XML Cite \textit{L. Yi} and \textit{B. Guo}, J. Comput. Appl. Math. 233, No. 2, 150--164 (2009; Zbl 1175.65090) Full Text: DOI
de Frutos, Javier; Novo, Julia Element-wise a posteriori estimates based on hierarchical bases for nonlinear parabolic problems. (English) Zbl 1118.65099 Int. J. Numer. Methods Eng. 63, No. 8, 1146-1173 (2005). Reviewer: Christian Grossmann (Dresden) MSC: 65M15 65M60 35K55 65M12 65M20 PDF BibTeX XML Cite \textit{J. de Frutos} and \textit{J. Novo}, Int. J. Numer. Methods Eng. 63, No. 8, 1146--1173 (2005; Zbl 1118.65099) Full Text: DOI
Cao, W.; Demkowicz, L. Optimal error estimate of a projection based interpolation for the \(p\)-version approximation in three dimensions. (English) Zbl 1092.65095 Comput. Math. Appl. 50, No. 3-4, 359-366 (2005). Reviewer: Jan Maes (Leuven) MSC: 65N15 65N30 35J25 PDF BibTeX XML Cite \textit{W. Cao} and \textit{L. Demkowicz}, Comput. Math. Appl. 50, No. 3--4, 359--366 (2005; Zbl 1092.65095) Full Text: DOI
Kashuba, E. V.; Rukavishnikov, V. A. On the \(p\)-version of the finite element method for the boundary value problem with singularity. (English. Russian summary) Zbl 1078.65104 Sib. Zh. Vychisl. Mat. 8, No. 1, 31-42 (2005). Reviewer: N. I. Alexandrova (Novosibirsk) MSC: 65N30 65N15 65N12 35J25 PDF BibTeX XML Cite \textit{E. V. Kashuba} and \textit{V. A. Rukavishnikov}, Sib. Zh. Vychisl. Mat. 8, No. 1, 31--42 (2005; Zbl 1078.65104)
Oh, Hae-Soo Accurate mode-separated energy release rates for delamination cracks. (English) Zbl 1047.74064 J. Comput. Phys. 193, No. 1, 86-114 (2004). MSC: 74S05 74R10 PDF BibTeX XML Cite \textit{H.-S. Oh}, J. Comput. Phys. 193, No. 1, 86--114 (2004; Zbl 1047.74064) Full Text: DOI
Beuchler, Sven AMLI preconditioner for the \(p\)-version of the FEM. (English) Zbl 1071.65059 Numer. Linear Algebra Appl. 10, No. 8, 721-732 (2003). Reviewer: Jan Chleboun (Praha) MSC: 65F35 65N30 PDF BibTeX XML Cite \textit{S. Beuchler}, Numer. Linear Algebra Appl. 10, No. 8, 721--732 (2003; Zbl 1071.65059) Full Text: DOI
Babuška, Ivo; Guo, Benqi Direct and inverse approximation theorems for the \(p\)-version of the finite element method in the framework of weighted Besov spaces. II: Optimal rate of convergence of the \(p\)-version finite element solutions. (English) Zbl 1026.65103 Math. Models Methods Appl. Sci. 12, No. 5, 689-719 (2002). MSC: 65N30 46E35 65N12 65N15 35J25 PDF BibTeX XML Cite \textit{I. Babuška} and \textit{B. Guo}, Math. Models Methods Appl. Sci. 12, No. 5, 689--719 (2002; Zbl 1026.65103) Full Text: DOI
Babuška, Ivo; Guo, Benqi Direct and inverse approximation theorems for the \(p\)-version of the finite element method in the framework of weighted Besov spaces. I: Approximability of functions in the weighted Besov spaces. (English) Zbl 1008.65078 SIAM J. Numer. Anal. 39, No. 5, 1512-1538 (2001). MSC: 65N30 35D10 65N25 46E35 PDF BibTeX XML Cite \textit{I. Babuška} and \textit{B. Guo}, SIAM J. Numer. Anal. 39, No. 5, 1512--1538 (2001; Zbl 1008.65078) Full Text: DOI
Bespalov, A. Yu.; Rukavishnikov, V. A. The use of singular functions in the \(h\)–\(p\) version of the finite element method for a Dirichlet problem with degeneration of the input data. (English. Russian summary) Zbl 0987.65118 Sib. Zh. Vychisl. Mat. 4, No. 3, 201-228 (2001). Reviewer: N.I.Alexandrova (Novosibirsk) MSC: 65N30 35J25 65N12 65N15 PDF BibTeX XML Cite \textit{A. Yu. Bespalov} and \textit{V. A. Rukavishnikov}, Sib. Zh. Vychisl. Mat. 4, No. 3, 201--228 (2001; Zbl 0987.65118)
Griebel, Michael; Schweitzer, Marc Alexander A particle-partition of unity method for the solution of elliptic, parabolic, and hyperbolic PDEs. (English) Zbl 0974.65090 SIAM J. Sci. Comput. 22, No. 3, 853-890 (2000). Reviewer: Thomas Sonar (Braunschweig) MSC: 65M60 65M25 65M12 65N30 65N12 35K15 35L15 35J25 PDF BibTeX XML Cite \textit{M. Griebel} and \textit{M. A. Schweitzer}, SIAM J. Sci. Comput. 22, No. 3, 853--890 (2000; Zbl 0974.65090) Full Text: DOI
Hu, Ning; Guo, Xian-Zhong; Katz, I. Norman Bounds for eigenvalues and condition numbers in the \(p\)-version of the finite element method. (English) Zbl 0907.65112 Math. Comput. 67, No. 224, 1423-1450 (1998). Reviewer: V.V.Kobkov (Novosibirsk) MSC: 65N30 65F35 35J25 PDF BibTeX XML Cite \textit{N. Hu} et al., Math. Comput. 67, No. 224, 1423--1450 (1998; Zbl 0907.65112) Full Text: DOI
Hu, Ning; Guo, Xian-zhong; Katz, I. Norman Multi-\(p\) preconditioners. (English) Zbl 0926.65046 SIAM J. Sci. Comput. 18, No. 6, 1676-1697 (1997). Reviewer: Myron Sussman (Bethel Park) MSC: 65F35 65F10 65N55 65N30 35J25 PDF BibTeX XML Cite \textit{N. Hu} et al., SIAM J. Sci. Comput. 18, No. 6, 1676--1697 (1997; Zbl 0926.65046) Full Text: DOI
Guo, Benqi; Cao, Weiming An iterative and parallel solver based on domain decomposition for the \(h-p\) version of the finite element method. (English) Zbl 0885.65129 J. Comput. Appl. Math. 83, No. 1, 71-85 (1997). Reviewer: P.Y.Yalamov (Russe) MSC: 65N55 35J05 65Y05 65N30 65F10 65F35 PDF BibTeX XML Cite \textit{B. Guo} and \textit{W. Cao}, J. Comput. Appl. Math. 83, No. 1, 71--85 (1997; Zbl 0885.65129) Full Text: DOI
Kim, Mi-Young; Park, Eun-Jae The \(p\)-version of the mixed-finite element method for nonlinear second-order elliptic problems. (English) Zbl 0841.65093 Numer. Methods Partial Differ. Equations 12, No. 1, 1-11 (1996). Reviewer: N.F.F.Ebecken (Rio de Janeiro) MSC: 65N30 65N15 35J65 PDF BibTeX XML Cite \textit{M.-Y. Kim} and \textit{E.-J. Park}, Numer. Methods Partial Differ. Equations 12, No. 1, 1--11 (1996; Zbl 0841.65093) Full Text: DOI
Maitre, Jean-François; Pourquier, Olivier Conditionings and diagonal preconditionings in the \(p\)- version of the finite element method for second order elliptic problems. (Conditionnements et préconditionnements diagonaux pour la \(p\)-version des méthodes d’éléments finis pour des problèmes elliptiques du second ordre.) (French. English summary) Zbl 0802.65109 C. R. Acad. Sci., Paris, Sér. I 318, No. 6, 583-586 (1994). MSC: 65N30 65F10 65F35 35J25 PDF BibTeX XML Cite \textit{J.-F. Maitre} and \textit{O. Pourquier}, C. R. Acad. Sci., Paris, Sér. I 318, No. 6, 583--586 (1994; Zbl 0802.65109)
Bernardi, Christine; Dauge, Monique; Maday, Yvon Trace liftings which preserve polynomials. (Relèvements de traces préservant les polynômes.) (French. Abridged English version) Zbl 0755.65103 C. R. Acad. Sci., Paris, Sér. I 315, No. 3, 333-338 (1992). MSC: 65N30 46G15 65N35 46E35 PDF BibTeX XML Cite \textit{C. Bernardi} et al., C. R. Acad. Sci., Paris, Sér. I 315, No. 3, 333--338 (1992; Zbl 0755.65103)
Babuška, I.; Craig, A.; Mandel, J.; Pitkäranta, J. Efficient preconditioning for the \(p\)-version finite element method in two dimensions. (English) Zbl 0754.65083 SIAM J. Numer. Anal. 28, No. 3, 624-661 (1991). Reviewer: T.Potra (Cluj-Napoca) MSC: 65N30 65F35 65F10 65N55 35J25 PDF BibTeX XML Cite \textit{I. Babuška} et al., SIAM J. Numer. Anal. 28, No. 3, 624--661 (1991; Zbl 0754.65083) Full Text: DOI
Zou, Jun; Huang, Hongci A posteriori error estimates for the \(h\)-\(p\) version of the finite element method for 1-D problems. (English. Chinese original) Zbl 0850.65157 Chin. J. Numer. Math. Appl. 12, No. 4, 75-90 (1990); translation from Math. Numer. Sin. 12, No. 3, 302-317 (1990). MSC: 65L70 65L60 65L10 34B05 PDF BibTeX XML Cite \textit{J. Zou} and \textit{H. Huang}, Chin. J. Numer. Math. Appl. 12, No. 4, 302--317 (1990; Zbl 0850.65157); translation from Math. Numer. Sin. 12, No. 3, 302--317 (1990)
Babuška, Ivo; Oh, Hae-Soo The p-version of the finite element method for domains with corners and for infinite domains. (English) Zbl 0717.65084 Numer. Methods Partial Differ. Equations 6, No. 4, 371-392 (1990). Reviewer: J.Weisel MSC: 65N30 65N15 35J25 PDF BibTeX XML Cite \textit{I. Babuška} and \textit{H.-S. Oh}, Numer. Methods Partial Differ. Equations 6, No. 4, 371--392 (1990; Zbl 0717.65084) Full Text: DOI
Suri, Manil The p-version of the finite element method for elliptic equations of order 2\(\ell\). (English) Zbl 0711.65094 RAIRO, Modélisation Math. Anal. Numér. 24, No. 2, 265-304 (1990). Reviewer: N.Herrmann MSC: 65N30 65N12 65N15 35J40 PDF BibTeX XML Cite \textit{M. Suri}, RAIRO, Modélisation Math. Anal. Numér. 24, No. 2, 265--304 (1990; Zbl 0711.65094) Full Text: DOI EuDML
Babuška, Ivo; Guo, B.; Suri, Manil Implementation of nonhomogeneous Dirichlet boundary conditions in the p version of the finite element method. (English) Zbl 0709.65079 IMPACT Comput. Sci. Eng. 1, No. 1, 36-63 (1989). Reviewer: I.N.Katz MSC: 65N30 35J25 PDF BibTeX XML Cite \textit{I. Babuška} et al., IMPACT Comput. Sci. Eng. 1, No. 1, 36--63 (1989; Zbl 0709.65079) Full Text: DOI
Alarcón, E. On the p-adaptive version of the boundary element method. (Spanish) Zbl 0707.65079 Proc. Math. Meet. in Honor of A. Dou, Madrid/Spain 1988, 41-49 (1989). Reviewer: J.P.Milasziewicz MSC: 65N38 65R20 65N30 35C15 35J25 45E10 PDF BibTeX XML
Stephan, E. P.; Suri, M. On the convergence of the p-version of the boundary element Galerkin method. (English) Zbl 0661.65118 Math. Comput. 52, No. 185, 31-48 (1989). Reviewer: C.-I.Gheorghiu MSC: 65N35 65N30 65R20 35C15 45E10 35J05 76Q05 PDF BibTeX XML Cite \textit{E. P. Stephan} and \textit{M. Suri}, Math. Comput. 52, No. 185, 31--48 (1989; Zbl 0661.65118) Full Text: DOI
Szabó, Barna A. Solution of electrostatic problems by the p-version of the finite element method. (English) Zbl 0651.65087 Commun. Appl. Numer. Methods 4, No. 4, 565-572 (1988). Reviewer: Ll.G.Chambers MSC: 65Z05 65N30 35Q99 18A30 PDF BibTeX XML Cite \textit{B. A. Szabó}, Commun. Appl. Numer. Methods 4, No. 4, 565--572 (1988; Zbl 0651.65087) Full Text: DOI
Guo, Ben Qi The h-p version of the finite element method for elliptic equations of order 2m. (English) Zbl 0628.65102 Numer. Math. 53, No. 1-2, 199-224 (1988). MSC: 65N30 74S05 35J40 PDF BibTeX XML Cite \textit{B. Q. Guo}, Numer. Math. 53, No. 1--2, 199--224 (1988; Zbl 0628.65102) Full Text: DOI EuDML
Szabó, Barna A. Solution of algebraic equations generated by the p-version of the finite element method. (English) Zbl 0627.65027 Appl. Math. Lett. 1, No. 1, 83-85 (1988). MSC: 65F10 65F15 65N30 PDF BibTeX XML Cite \textit{B. A. Szabó}, Appl. Math. Lett. 1, No. 1, 83--85 (1988; Zbl 0627.65027) Full Text: DOI
Babuška, I.; Suri, Manil The optimal convergence rate of the p-version of the finite element method. (English) Zbl 0637.65103 SIAM J. Numer. Anal. 24, 750-776 (1987). Reviewer: F.v.Finckenstein MSC: 65N30 65N15 35J25 PDF BibTeX XML Cite \textit{I. Babuška} and \textit{M. Suri}, SIAM J. Numer. Anal. 24, 750--776 (1987; Zbl 0637.65103) Full Text: DOI
Babuška, I.; Suri, Manil The h-p version of the finite element method with quasiuniform meshes. (English) Zbl 0623.65113 RAIRO, Modélisation Math. Anal. Numér. 21, 199-238 (1987). Reviewer: J.Weisel MSC: 65N30 74S05 35J05 74B05 65N15 PDF BibTeX XML Cite \textit{I. Babuška} and \textit{M. Suri}, RAIRO, Modélisation Math. Anal. Numér. 21, 199--238 (1987; Zbl 0623.65113) Full Text: DOI EuDML
Eriksson, Kenneth Some error estimates for the p-version of the finite element method. (English) Zbl 0625.65072 SIAM J. Numer. Anal. 23, 403-411 (1986). Reviewer: Myron Sussman MSC: 65L10 65L60 65N30 34B05 PDF BibTeX XML Cite \textit{K. Eriksson}, SIAM J. Numer. Anal. 23, 403--411 (1986; Zbl 0625.65072) Full Text: DOI
Dorr, Milo R. The approximation of solutions of elliptic boundary-value problems via the p-version of the finite element method. (English) Zbl 0617.65109 SIAM J. Numer. Anal. 23, 58-77 (1986). Reviewer: J.Lovíšek MSC: 65N30 74S05 74B05 35J25 PDF BibTeX XML Cite \textit{M. R. Dorr}, SIAM J. Numer. Anal. 23, 58--77 (1986; Zbl 0617.65109) Full Text: DOI
Gui, W.; Babuška, I. The h, p and h-p versions of the finite element method in 1 dimension. I. The error analysis of the p-version. (English) Zbl 0614.65088 Numer. Math. 49, 577-612 (1986). Reviewer: C.-I.Gheorghiu MSC: 65L10 65L60 30E10 41A50 34B05 PDF BibTeX XML Cite \textit{W. Gui} and \textit{I. Babuška}, Numer. Math. 49, 577--612 (1986; Zbl 0614.65088) Full Text: DOI EuDML
Bennighof, J. K.; Meirovitch, L. Eigenvalue convergence in the finite element method. (English) Zbl 0597.73078 Int. J. Numer. Methods Eng. 23, 2153-2165 (1986). MSC: 74S05 PDF BibTeX XML Cite \textit{J. K. Bennighof} and \textit{L. Meirovitch}, Int. J. Numer. Methods Eng. 23, 2153--2165 (1986; Zbl 0597.73078) Full Text: DOI
Dorr, Milo R. The approximation theory for the p-version of the finite element method. (English) Zbl 0572.65074 SIAM J. Numer. Anal. 21, 1180-1207 (1984). Reviewer: M.Sussman MSC: 65L60 65N30 34B05 35J05 PDF BibTeX XML Cite \textit{M. R. Dorr}, SIAM J. Numer. Anal. 21, 1180--1207 (1984; Zbl 0572.65074) Full Text: DOI
Dunavant, David A.; Szabo, Barna A. A posteriori error indicators for the p-version of the finite element method. (English) Zbl 0526.65081 Int. J. Numer. Methods Eng. 19, 1851-1870 (1983). MSC: 65N30 65N15 74S05 35K25 PDF BibTeX XML Cite \textit{D. A. Dunavant} and \textit{B. A. Szabo}, Int. J. Numer. Methods Eng. 19, 1851--1870 (1983; Zbl 0526.65081) Full Text: DOI