ALBERT—Software for scientific computations and applications. Adaptive finite element methods (FEMs) are a modern, widely used tool which make realistic computations feasible, even in three space dimensions. We describe the basic ideas and ingredients of adaptive FEM and the implementation of our toolbox ALBERT. The design of ALBERT is based on the natural hierarchy of locally refined meshes and an abstract concept of general finite element spaces. As a result, dimension independent programming of applications is possible. Numerical results from applications in two and three space dimensions demonstrate the flexibility of ALBERT.

References in zbMATH (referenced in 72 articles , 1 standard article )

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  1. Cui, Ming; Chen, Zhangxin; Ewing, Richard E.; Qin, Guan; Chen, Hongsen: Reliable and efficient error control for an adaptive Galerkin-characteristic method for convection-dominated diffusion problems (2012)
  2. Kreuzer, Christian; Möller, Christian A.; Schmidt, Alfred; Siebert, Kunibert G.: Design and convergence analysis for an adaptive discretization of the heat equation (2012)
  3. Mekchay, Khamron: Application of adaptive finite element method for elliptic partial differential equations to the Laplace Beltrami operator on graphs (2012)
  4. Siebert, Kunibert G.: Mathematically founded design of adaptive finite element software (2012)
  5. Zhong, Liuqiang; Chen, Long; Shu, Shi; Wittum, Gabriel; Xu, Jinchao: Convergence and optimality of adaptive edge finite element methods for time-harmonic Maxwell equations (2012)
  6. Dzhumadil’daev, Askar; Zusmanovich, Pasha: The alternative operad is not Koszul (2011)
  7. Fuhrmann, Jürgen; Linke, Alexander; Langmach, Hartmut: A numerical method for mass conservative coupling between fluid flow and solute transport (2011)
  8. Baňas, L’ubomír: An efficient multigrid preconditioner for Maxwell’s equations in micromagnetism (2010)
  9. Banas, Lubomír; Prohl, Andreas: Convergent finite element discretization of the multi-fluid nonstationary incompressible magnetohydrodynamics equations (2010)
  10. Baňas, L’ubomír; Prohl, Andreas; Schätzle, Reiner: Finite element approximations of harmonic map heat flows and wave maps into spheres of nonconstant radii (2010)
  11. Ern, Alexandre; Vohralík, Martin: A posteriori error estimation based on potential and flux reconstruction for the heat equation (2010)
  12. Baňas, L’ubomír; Nürnberg, Robert: Phase field computations for surface diffusion and void electromigration in $\mathbbR^3$ (2009)
  13. Giani, S.; Graham, I.G.: A convergent adaptive method for elliptic eigenvalue problems (2009)
  14. Picasso, M.: A stopping criterion for the conjugate gradient algorithm in the framework of anisotropic adaptive finite elements (2009)
  15. Zhang, Jian; Du, Qiang: Numerical studies of discrete approximations to the Allen-Cahn equation in the sharp interface limit (2009)
  16. Baňas, L’ubomír; Bartels, Sören; Prohl, Andreas: A convergent implicit finite element discretization of the Maxwell -- Landau -- Lifshitz -- Gilbert equation (2008)
  17. Baňas, Ľubomír; Nürnberg, Robert: Finite element approximation of a three dimensional phase field model for void electromigration (2008)
  18. Barrett, John W.; El Alaoui, Linda: Finite element approximation of a two-layered liquid film in the presence of insoluble surfactants (2008)
  19. Chen, Junqing; Chen, Zhiming: An adaptive perfectly matched layer technique for 3-D time-harmonic electromagnetic scattering problems (2008)
  20. Köster, Daniel; Kriessl, Oliver; Siebert, Kunibert G.: Design of finite element tools for coupled surface and volume meshes (2008)

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