Caro, Felipe V.; Darrigrand, Vincent; Alvarez-Aramberri, Julen; Alberdi, Elisabete; Pardo, David A painless multi-level automatic goal-oriented \(hp\)-adaptive coarsening strategy for elliptic and non-elliptic problems. (English) Zbl 1507.74454 Comput. Methods Appl. Mech. Eng. 401, Part B, Article ID 115641, 27 p. (2022). MSC: 74S05 65N30 PDFBibTeX XMLCite \textit{F. V. Caro} et al., Comput. Methods Appl. Mech. Eng. 401, Part B, Article ID 115641, 27 p. (2022; Zbl 1507.74454) Full Text: DOI
Appella, Simone; Budd, Chris; Pryer, Tristan An adaptive conservative moving mesh method. (English) Zbl 1507.65168 Sevilla, Rubén (ed.) et al., Mesh generation and adaptation. Cutting-edge techniques. Cham: Springer. SEMA SIMAI Springer Ser. 30, 277-299 (2022). MSC: 65M50 PDFBibTeX XMLCite \textit{S. Appella} et al., SEMA SIMAI Springer Ser. 30, 277--299 (2022; Zbl 1507.65168) Full Text: DOI
Fortunato, Daniel; Hale, Nicholas; Townsend, Alex The ultraspherical spectral element method. (English) Zbl 07513834 J. Comput. Phys. 436, Article ID 110087, 20 p. (2021). MSC: 65Nxx 35Jxx 65Fxx PDFBibTeX XMLCite \textit{D. Fortunato} et al., J. Comput. Phys. 436, Article ID 110087, 20 p. (2021; Zbl 07513834) Full Text: DOI arXiv
Vlasák, Miloslav On polynomial robustness of flux reconstructions. (English) Zbl 07217103 Appl. Math., Praha 65, No. 2, 153-172 (2020). MSC: 65N15 65N30 PDFBibTeX XMLCite \textit{M. Vlasák}, Appl. Math., Praha 65, No. 2, 153--172 (2020; Zbl 07217103) Full Text: DOI
Ghesmati, Arezou; Bangerth, Wolfgang; Turcksin, Bruno Residual-based a posteriori error estimation for \(hp\)-adaptive finite element methods for the Stokes equations. (English) Zbl 1435.65201 J. Numer. Math. 27, No. 4, 237-252 (2019). MSC: 65N30 65N15 76D07 65N50 PDFBibTeX XMLCite \textit{A. Ghesmati} et al., J. Numer. Math. 27, No. 4, 237--252 (2019; Zbl 1435.65201) Full Text: DOI arXiv
Guo, Ruchi; Lin, Tao A higher degree immersed finite element method based on a Cauchy extension for elliptic interface problems. (English) Zbl 1420.65122 SIAM J. Numer. Anal. 57, No. 4, 1545-1573 (2019). MSC: 65N30 35R05 35J25 65N12 PDFBibTeX XMLCite \textit{R. Guo} and \textit{T. Lin}, SIAM J. Numer. Anal. 57, No. 4, 1545--1573 (2019; Zbl 1420.65122) Full Text: DOI
Liu, Zhengguang; Cheng, Aijie; Wang, Hong An \(hp\)-Galerkin method with fast solution for linear peridynamic models in one dimension. (English) Zbl 1372.65310 Comput. Math. Appl. 73, No. 7, 1546-1565 (2017). MSC: 65N30 65T50 65N50 35J25 15B05 PDFBibTeX XMLCite \textit{Z. Liu} et al., Comput. Math. Appl. 73, No. 7, 1546--1565 (2017; Zbl 1372.65310) Full Text: DOI
Carson, Hugh A.; Darmofal, David L.; Galbraith, Marshall C.; Allmaras, Steven R. Analysis of output-based error estimation for finite element methods. (English) Zbl 1367.65166 Appl. Numer. Math. 118, 182-202 (2017). MSC: 65N30 35J05 65N12 65N15 PDFBibTeX XMLCite \textit{H. A. Carson} et al., Appl. Numer. Math. 118, 182--202 (2017; Zbl 1367.65166) Full Text: DOI
Canuto, Claudio; Nochetto, Ricardo H.; Stevenson, Rob; Verani, Marco Convergence and optimality of \({\mathbf {hp}}\)-AFEM. (English) Zbl 1364.65241 Numer. Math. 135, No. 4, 1073-1119 (2017). MSC: 65N30 65N12 65N50 PDFBibTeX XMLCite \textit{C. Canuto} et al., Numer. Math. 135, No. 4, 1073--1119 (2017; Zbl 1364.65241) Full Text: DOI arXiv
Houston, Paul; Wihler, Thomas P. Adaptive energy minimisation for \(hp\)-finite element methods. (English) Zbl 1443.65335 Comput. Math. Appl. 71, No. 4, 977-990 (2016). MSC: 65N30 65N35 PDFBibTeX XMLCite \textit{P. Houston} and \textit{T. P. Wihler}, Comput. Math. Appl. 71, No. 4, 977--990 (2016; Zbl 1443.65335) Full Text: DOI arXiv
Armentano, María G.; Moreno, Verónica Interpolation in Jacobi-weighted spaces and its application to a posteriori error estimations of the \(p\)-version of the finite element method. (English) Zbl 1348.65151 Appl. Numer. Math. 109, 184-207 (2016). MSC: 65N15 35J25 65N30 PDFBibTeX XMLCite \textit{M. G. Armentano} and \textit{V. Moreno}, Appl. Numer. Math. 109, 184--207 (2016; Zbl 1348.65151) Full Text: DOI arXiv
Bürg, Markus; Schröder, Andreas A posteriori error control of \(hp\)-finite elements for variational inequalities of the first and second kind. (English) Zbl 1443.65314 Comput. Math. Appl. 70, No. 12, 2783-2802 (2015). MSC: 65N30 65K15 PDFBibTeX XMLCite \textit{M. Bürg} and \textit{A. Schröder}, Comput. Math. Appl. 70, No. 12, 2783--2802 (2015; Zbl 1443.65314) Full Text: DOI
Armentano, M. G.; Padra, C.; Scheble, M. An \(hp\) finite element adaptive scheme to solve the Poisson problem on curved domains. (English) Zbl 1322.65103 Comput. Appl. Math. 34, No. 2, 705-727 (2015). Reviewer: Abdallah Bradji (Annaba) MSC: 65N30 65N15 65N50 35J05 PDFBibTeX XMLCite \textit{M. G. Armentano} et al., Comput. Appl. Math. 34, No. 2, 705--727 (2015; Zbl 1322.65103) Full Text: DOI
Gonçalves, João L.; Gomes, Sônia M.; Devloo, Philippe R. B. A goal-oriented \(hp\)-adaptive discontinuous Galerkin approach for biharmonic problems. (English) Zbl 1352.65504 Int. J. Numer. Methods Eng. 97, No. 4, 274-297 (2014). MSC: 65N30 65N15 65N50 PDFBibTeX XMLCite \textit{J. L. Gonçalves} et al., Int. J. Numer. Methods Eng. 97, No. 4, 274--297 (2014; Zbl 1352.65504) Full Text: DOI
Fankhauser, Thomas; Wihler, Thomas P.; Wirz, Marcel The \(hp\)-adaptive FEM based on continuous Sobolev embeddings: isotropic refinements. (English) Zbl 1416.65443 Comput. Math. Appl. 67, No. 4, 854-868 (2014). MSC: 65N30 65N50 PDFBibTeX XMLCite \textit{T. Fankhauser} et al., Comput. Math. Appl. 67, No. 4, 854--868 (2014; Zbl 1416.65443) Full Text: DOI
Schnepp, Sascha M. Error-driven dynamical \(hp\)-meshes with the discontinuous Galerkin method for three-dimensional wave propagation problems. (English) Zbl 1330.78019 J. Comput. Appl. Math. 270, 353-368 (2014). Reviewer: Teodora-Liliana Rădulescu (Craiova) MSC: 78M10 78M15 78A50 65M60 65M50 PDFBibTeX XMLCite \textit{S. M. Schnepp}, J. Comput. Appl. Math. 270, 353--368 (2014; Zbl 1330.78019) Full Text: DOI arXiv
Gomez-Revuelto, Ignacio; Garcia-Castillo, Luis E.; Llorente-Romano, Sergio; Pardo, David A three-dimensional self-adaptive \(hp\) finite element method for the characterization of waveguide discontinuities. (English) Zbl 1348.78025 Comput. Methods Appl. Mech. Eng. 249-252, 62-74 (2012). MSC: 78M10 78A50 65N30 PDFBibTeX XMLCite \textit{I. Gomez-Revuelto} et al., Comput. Methods Appl. Mech. Eng. 249--252, 62--74 (2012; Zbl 1348.78025) Full Text: DOI
Liu, Hongfu; Chen, Shaofei; Shen, Lincheng; Chen, Jing An integrated multicriterion \(hp\)-adaptive pseudospectral method for direct optimal control problems solving. (English) Zbl 1264.65125 Math. Probl. Eng. 2012, Article ID 760890, 22 p. (2012). MSC: 65L60 49M25 PDFBibTeX XMLCite \textit{H. Liu} et al., Math. Probl. Eng. 2012, Article ID 760890, 22 p. (2012; Zbl 1264.65125) Full Text: DOI
Ledger, P. D. \(hp\)-finite element discretisation of the electrical impedance tomography problem. (English) Zbl 1253.78044 Comput. Methods Appl. Mech. Eng. 225-228, 154-176 (2012). MSC: 78A70 78M10 65M60 94A08 94A20 PDFBibTeX XMLCite \textit{P. D. Ledger}, Comput. Methods Appl. Mech. Eng. 225--228, 154--176 (2012; Zbl 1253.78044) Full Text: DOI
Bank, Randolph E.; Nguyen, Hieu \(hp\) adaptive finite elements based on derivative recovery and superconvergence. (English) Zbl 1380.65358 Comput. Vis. Sci. 14, No. 6, 287-299 (2011). MSC: 65N30 65N50 65N55 PDFBibTeX XMLCite \textit{R. E. Bank} and \textit{H. Nguyen}, Comput. Vis. Sci. 14, No. 6, 287--299 (2011; Zbl 1380.65358) Full Text: DOI
Bürg, M.; Dörfler, W. Convergence of an adaptive \(hp\) finite element strategy in higher space-dimensions. (English) Zbl 1230.65115 Appl. Numer. Math. 61, No. 11, 1132-1146 (2011). Reviewer: Abdallah Bradji (Annaba) MSC: 65N12 65N30 35J25 65N50 PDFBibTeX XMLCite \textit{M. Bürg} and \textit{W. Dörfler}, Appl. Numer. Math. 61, No. 11, 1132--1146 (2011; Zbl 1230.65115) Full Text: DOI
Jimack, Peter K.; Kirby, Robert M. Towards the development of an \(h\)-\(p\)-refinement strategy based upon error estimate sensitivity. (English) Zbl 1433.65202 Comput. Fluids 46, No. 1, 277-281 (2011). MSC: 65M50 65M15 76M99 PDFBibTeX XMLCite \textit{P. K. Jimack} and \textit{R. M. Kirby}, Comput. Fluids 46, No. 1, 277--281 (2011; Zbl 1433.65202) Full Text: DOI
Wihler, Thomas P. An \(hp\)-adaptive strategy based on continuous Sobolev embeddings. (English) Zbl 1209.65080 J. Comput. Appl. Math. 235, No. 8, 2731-2739 (2011). MSC: 65L10 34B05 65L60 65L70 46E35 PDFBibTeX XMLCite \textit{T. P. Wihler}, J. Comput. Appl. Math. 235, No. 8, 2731--2739 (2011; Zbl 1209.65080) Full Text: DOI
Armentano, M. G.; Padra, C.; Rodríguez, R.; Scheble, M. An hp finite element adaptive scheme to solve the Laplace model for fluid-solid vibrations. (English) Zbl 1225.74078 Comput. Methods Appl. Mech. Eng. 200, No. 1-4, 178-188 (2011). MSC: 74S05 74F10 PDFBibTeX XMLCite \textit{M. G. Armentano} et al., Comput. Methods Appl. Mech. Eng. 200, No. 1--4, 178--188 (2010; Zbl 1225.74078) Full Text: DOI
Brown, Jed Efficient nonlinear solvers for nodal high-order finite elements in 3D. (English) Zbl 1203.65245 J. Sci. Comput. 45, No. 1-3, 48-63 (2010). MSC: 65N30 65N22 PDFBibTeX XMLCite \textit{J. Brown}, J. Sci. Comput. 45, No. 1--3, 48--63 (2010; Zbl 1203.65245) Full Text: DOI Link
Schmidt, K.; Kauf, P. Computation of the band structure of two-dimensional photonic crystals with \(hp\) finite elements. (English) Zbl 1157.78355 Comput. Methods Appl. Mech. Eng. 198, No. 13-14, 1249-1259 (2009). MSC: 78M10 65N30 PDFBibTeX XMLCite \textit{K. Schmidt} and \textit{P. Kauf}, Comput. Methods Appl. Mech. Eng. 198, No. 13--14, 1249--1259 (2009; Zbl 1157.78355) Full Text: DOI
Harutyunyan, D.; Izsák, F.; van der Vegt, J. J. W.; Botchev, M. A. Adaptive finite element techniques for the Maxwell equations using implicit a posteriori error estimates. (English) Zbl 1194.78054 Comput. Methods Appl. Mech. Eng. 197, No. 17-18, 1620-1638 (2008). MSC: 78M10 78A25 PDFBibTeX XMLCite \textit{D. Harutyunyan} et al., Comput. Methods Appl. Mech. Eng. 197, No. 17--18, 1620--1638 (2008; Zbl 1194.78054) Full Text: DOI
Kurtz, J.; Demkowicz, L. A fully automatic \(hp\)-adaptivity for elliptic PDEs in three dimensions. (English) Zbl 1173.65357 Comput. Methods Appl. Mech. Eng. 196, No. 37-40, 3534-3545 (2007). MSC: 65N30 65N50 PDFBibTeX XMLCite \textit{J. Kurtz} and \textit{L. Demkowicz}, Comput. Methods Appl. Mech. Eng. 196, No. 37--40, 3534--3545 (2007; Zbl 1173.65357) Full Text: DOI
Eibner, T.; Melenk, J. M. An adaptive strategy for \(hp\)-FEM based on testing for analyticity. (English) Zbl 1163.65331 Comput. Mech. 39, No. 5, 575-595 (2007). MSC: 65N30 65N15 35J05 PDFBibTeX XMLCite \textit{T. Eibner} and \textit{J. M. Melenk}, Comput. Mech. 39, No. 5, 575--595 (2007; Zbl 1163.65331) Full Text: DOI
Dörfler, W.; Heuveline, V. Convergence of an adaptive \( hp\) finite element strategy in one space dimension. (English) Zbl 1123.65079 Appl. Numer. Math. 57, No. 10, 1108-1124 (2007). Reviewer: Kai Diethelm (Braunschweig) MSC: 65L60 65L50 65L10 65L70 65L20 34B05 PDFBibTeX XMLCite \textit{W. Dörfler} and \textit{V. Heuveline}, Appl. Numer. Math. 57, No. 10, 1108--1124 (2007; Zbl 1123.65079) Full Text: DOI
Houston, Paul; Süli, Endre A note on the design of \(hp\)-adaptive finite element methods for elliptic partial differential equations. (English) Zbl 1074.65131 Comput. Methods Appl. Mech. Eng. 194, No. 2-5, 229-243 (2005). Reviewer: H. P. Dikshit (New Delhi) MSC: 65N30 65N15 35J25 PDFBibTeX XMLCite \textit{P. Houston} and \textit{E. Süli}, Comput. Methods Appl. Mech. Eng. 194, No. 2--5, 229--243 (2005; Zbl 1074.65131) Full Text: DOI
Heuveline, V.; Rannacher, R. Duality-based adaptivity in the \(hp\)-finite element method. (English) Zbl 1050.65111 J. Numer. Math. 11, No. 2, 95-113 (2003). Reviewer: Isaac Yevzerov (Kyïv) MSC: 65N30 35J05 65N15 PDFBibTeX XMLCite \textit{V. Heuveline} and \textit{R. Rannacher}, J. Numer. Math. 11, No. 2, 95--113 (2003; Zbl 1050.65111) Full Text: DOI
Houston, Paul; Senior, Bill; Süli, Endre \(hp\)-discontinuous Galerkin finite element methods for hyperbolic problems: Error analysis and adaptivity. (English) Zbl 1021.76027 Int. J. Numer. Methods Fluids 40, No. 1-2, 153-169 (2002). MSC: 76M10 76N15 PDFBibTeX XMLCite \textit{P. Houston} et al., Int. J. Numer. Methods Fluids 40, No. 1--2, 153--169 (2002; Zbl 1021.76027) Full Text: DOI
Heuer, Norbert An \(hp\)-adaptive refinement strategy for hypersingular operators on surfaces. (English) Zbl 0999.65139 Numer. Methods Partial Differ. Equations 18, No. 3, 396-419 (2002). Reviewer: Calin Ioan Gheorghiu (Cluj-Napoca) MSC: 65N38 65N12 65N50 35J25 PDFBibTeX XMLCite \textit{N. Heuer}, Numer. Methods Partial Differ. Equations 18, No. 3, 396--419 (2002; Zbl 0999.65139) Full Text: DOI
Mackerle, Jaroslav Error estimates and adaptive finite element methods. A bibliography (1990–2000). (English) Zbl 0985.65140 Eng. Comput. (Bradf.) 18, No. 5-6, 802-914 (2001). MSC: 65N30 74S05 65N15 65-00 74-00 65M60 65M15 78M10 PDFBibTeX XMLCite \textit{J. Mackerle}, Eng. Comput. (Bradf.) 18, No. 5--6, 802--914 (2001; Zbl 0985.65140) Full Text: DOI
Carstensen, C.; Faermann, B. Mathematical foundation of a posteriori error estimates and adaptive mesh-refining algorithms for boundary integral equations of the first kind. (English) Zbl 1007.65100 Eng. Anal. Bound. Elem. 25, No. 7, 497-509 (2001). MSC: 65N38 65N12 65N15 65N50 35J25 65R20 45E10 PDFBibTeX XMLCite \textit{C. Carstensen} and \textit{B. Faermann}, Eng. Anal. Bound. Elem. 25, No. 7, 497--509 (2001; Zbl 1007.65100) Full Text: DOI
Ainsworth, Mark; Senior, Bill Aspects of an adaptive \(hp\)-finite element method: Adaptive strategy, conforming approximation and efficient solvers. (English) Zbl 0906.73057 Comput. Methods Appl. Mech. Eng. 150, No. 1-4, 65-87 (1997). MSC: 74S05 74R99 74B05 65N50 PDFBibTeX XMLCite \textit{M. Ainsworth} and \textit{B. Senior}, Comput. Methods Appl. Mech. Eng. 150, No. 1--4, 65--87 (1997; Zbl 0906.73057) Full Text: DOI