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Space-time adaptive $h p$ -FEM: Methodology overview

Šolín, Pavel, Segeth, Karel, Doležel, Ivo (2008)

Programs and Algorithms of Numerical Mathematics

We present a new class of self-adaptive higher-order finite element methods ( $h p$ -FEM) which are free of analytical error estimates and thus work equally well for virtually all PDE problems ranging from simple linear elliptic equations to complex time-dependent nonlinear multiphysics coupled problems. The methods do not contain any tuning parameters and work reliably with both low- and high-order finite elements. The methodology was used to solve various types of problems including thermoelasticity,...

Spatially nonhomogeneous pattern generated by homoclinic/equilibrium bifurcations

Lin, Xiao-Biao (1994)

Equadiff 8

Special issue: Editorial

Angela Handlovičová, Oľga Nánásiová, Jan Ámos Víšek (2007)

Kybernetika

Special issue: Editorial [Czech and Slovak Twin Seminar in Applied Mathematics 2006]

Michal Beneš, Masato Kimura, Tatsuyuki Nakaki (2007)

Kybernetika

Spectral theory of nonlinear operators

Fučík, Svatopluk, Nečas, Jindřich (1973)

Proceedings of Equadiff III

Spherically symmetric solutions to a model for interface motion by interface diffusion

Zhu, Peicheng (2013)

Applications of Mathematics 2013

The existence of spherically symmetric solutions is proved for a new phase-field model that describes the motion of an interface in an elastically deformable solid, here the motion is driven by configurational forces. The model is an elliptic-parabolic coupled system which consists of a linear elasticity system and a non-linear evolution equation of the order parameter. The non-linear equation is non-uniformly parabolic and is of fourth order. One typical application is sintering.