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- Pavel Solín, David Andrs, Jakub Cervený, Miroslav Simko
- J. Computational Applied Mathematics
- 2010

- Pavel Solín, Jakub Cervený, Lenka Dubcova, David Andrs
- J. Computational Applied Mathematics
- 2010

In linear thermoelasticity models, the temperature T and the displacement components u1, u2 exhibit large qualitative differences: While T typically is very smooth everywhere in the domain, the displacements u1, u2 have singular gradients (stresses) at re-entrant corners and edges. The mesh must be extremely fine in these areas so that stress intensity… (More)

- Pavel Kus, Pavel Solín, David Andrs
- J. Computational Applied Mathematics
- 2014

In this paper we discuss constrained approximation with arbitrary-level hanging nodes in adaptive higher-order finite element methods (hp-FEM) for three-dimensional problems. This technique enables using highly irregular meshes, and it greatly simplifies the design of adaptive algorithms as it prevents refinements from propagating recursively through the… (More)

- Liangzhe Zhang, Michael R. Tonks, +4 authors Bulent S. Biner
- J. Comput. Physics
- 2013

The Cahn–Hilliard (CH) equation is a time-dependent fourth-order partial differential equation (PDE). When solving the CH equation via the finite element method (FEM), the domain is discretized by C-continuous basis functions or the equation is split into a pair of second-order PDEs, and discretized via C-continuous basis functions. In the current work, a… (More)

We present a novel compression algorithm for 2D scientific data and images based on exponentially-convergent adaptive higher-order finite element methods (FEM). So far, FEM has been used mainly for the solution of partial differential equations (PDE), but we show that it can be applied to data and image compression easily. The adaptive compression algorithm… (More)

- Pavel Solin, David Andrs
- 2007

We present a new compression algorithm for two-and three-dimensional volume data (such as images or continuous fields). The technique is based on orthogonal projection of the data to spaces of polynomial functions and it works analogously to adaptive hp-FEM for the solution of partial differential equations. The algorithm has extremely high compression… (More)

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