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The thesis is concerned with theoretical and practical aspects of the hp-adaptive finite element method for solving elliptic and electromagnetic problems described by partial differential equations in three spatial dimensions. Besides the standard element refinements, the hp-adaptivity allows independent adaptation of degrees of the polynomial approximation(More)
We propose a novel, highly efficient and accurate space and time adaptive higher-order finite element method (hp-FEM) for evolutionary microwave heating problems. Since the electric field E and temperature field T are very different in nature, we approximate them on individual meshes that change dynamically in time independently of each other. Although the(More)
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)
New code Agros2D for 2D numerical solution of coupled problems is presented. This code is based on the fully adaptive higher-order finite element method and works with library Hermes2D containing the most advanced numerical algorithms for the numerical processing of systems of second-order partial differential equations. It is characterized by several quite(More)
The process of induction heating of cylindrical nonmagnetic billets is modeled and optimized. An unmovable billet is placed in rotating magnetic field generated by permanent magnets fixed in an external rotor driven by an asynchronous motor by means of a teeth gear. The coupled model of the problem consisting of two partial differential equations describing(More)
We study the effect of adaptive mesh refinement on a parallel domain decomposition solver of a linear system of algebraic equations. These concepts need to be combined within a parallel adaptive finite element software. A prototype implementation is presented for this purpose. It uses adaptive mesh refinement with one level of hanging nodes. Two and(More)
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