[3] Ainsworth, M., Rankin, R.:
Fully computable error bounds for discontinuous Galerkin finite element approximations on meshes with an arbitrary number of levels of hanging nodes. SIAM J. Numer. Anal. 47 (2010), 4112-4141.
DOI 10.1137/080725945 |
MR 2585181 |
Zbl 1208.65155
[12] Bergman, S., Schiffer, M.:
Kernel Functions and Elliptic Differential Equations in Mathematical Physics. Pure and Applied Mathematics 4, Academic Press, New York (1953).
MR 0054140 |
Zbl 0053.39003
[16] Braess, D., Fraunholz, T., Hoppe, R. H. W.:
An equilibrated a posteriori error estimator for the interior penalty discontinuous Galerkin method. SIAM J. Numer. Anal. 52 (2014), 2121-2136.
DOI 10.1137/130916540 |
MR 3249368 |
Zbl 1302.65239
[17] Bramble, J. H., Osborn, J. E.:
Approximation of Steklov eigenvalues of non-selfadjoint second order elliptic operators. The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations Proc. Sympos. Univ. Maryland, Baltimore, 1972, Academic Press, New York (1972), 387-408.
DOI 10.1016/b978-0-12-068650-6.50019-8 |
MR 0431740 |
Zbl 0264.35055
[19] Chen, L., Zhang, C.: AFEM@matlab: a Matlab package of adaptive finite element methods. Technical report, University of Maryland at College Park (2006).
[21] Conca, C., Planchard, J., Vanninathan, M.:
Fluids and Periodic Structures. Research in Applied Mathematics, Wiley, Chichester; Masson, Paris (1995).
MR 1652238 |
Zbl 0910.76002
[22] Dolejší, V., Šebestová, I., Vohralík, M.:
Algebraic and discretization error estimation by equilibrated fluxes for discontinuous Galerkin methods on nonmatching grids. J. Sci. Comput. 64 (2015), 1-34.
DOI 10.1007/s10915-014-9921-2 |
MR 3353932 |
Zbl 1326.65147
[26] Giani, S., Hall, E. J. C.:
An a posteriori error estimator for $hp$-adaptive discontinuous Galerkin methods for elliptic eigenvalue problems. Math. Models Methods Appl. Sci. 22 (2012), 1250030, 35 pages.
DOI 10.1142/S0218202512500303 |
MR 2974168 |
Zbl 1257.65062
[28] Hinton, D. B., Shaw, J. K.:
Differential operators with spectral parameter incompletely in the boundary conditions. Funkc. Ekvacioj, Ser. Int. 33 (1990), 363-385.
MR 1086767 |
Zbl 0715.34133
[29] Hoppe, R. H. W., Kanschat, G., Warburton, T.:
Convergence analysis of an adaptive interior penalty discontinuous Galerkin method. SIAM J. Numer. Anal. 47 (2008), 534-550.
DOI 10.1137/070704599 |
MR 2475951 |
Zbl 1189.65274
[30] Houston, P., Perugia, I., Schötzau, D.:
An a posteriori error indicator for discontinuous Galerkin discretizations of $H$(curl)-elliptic partial differential equations. IMA J. Numer. Anal. 27 (2007), 122-150.
DOI 10.1093/imanum/drl012 |
MR 2289274 |
Zbl 1148.65088
[31] Houston, P., Schötzau, D., Wihler, T. P.:
Energy norm a posteriori error estimation of $hp$-adaptive discontinuous Galerkin methods for elliptic problems. Math. Models Methods Appl. Sci. 17 (2007), 33-62.
DOI 10.1142/S0218202507001826 |
MR 2290408 |
Zbl 1116.65115
[33] Karakashian, O. A., Pascal, F.:
Convergence of adaptive discontinuous Galerkin approximations of second-order elliptic problems. SIAM J. Numer. Anal. 45 (2007), 641-665.
DOI 10.1137/05063979X |
MR 2300291 |
Zbl 1140.65083
[36] Lin, Q., Xie, H.:
A multilevel correction type of adaptive finite element method for Steklov eigenvalue problems. Proceedings of the International Conference Applications of Mathematics, Praha (J. Brandts et al., eds.) Academy of Sciences of the Czech Republic, Institute of Mathematics, Praha (2012), 134-143.
MR 3204407 |
Zbl 1313.65298
[45] Verfürth, R.: A Review of a Posteriori Estimation and Adaptive Mesh-Refinement Techniques. Wiley-Teubner Series Advances in Numerical Mathematics, John Wiley, Chichester (1996).
[47] Yang, J., Chen, Y.:
A unified a posteriori error analysis for discontinuous Galerkin approximations of reactive transport equations. J. Comput. Math. 24 (2006), 425-434.
MR 2229721 |
Zbl 1142.76034
[49] Zeng, Y., Chen, J., Wang, F.:
A posteriori error estimates of a weakly over-penalized symmetric interior penalty method for elliptic eigenvalue problems. East Asian J. Appl. Math. 5 (2015), 327-341.
DOI 10.4208/eajam.060415.230915a |
MR 3421807