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Local nonobtuse tetrahedral refinements around an edge
In this note we show how to generate and conformly refine nonobtuse tetrahedral meshes locally around and towards an edge so that all dihedral angles of all resulting tetrahedra remain nonobtuse. The proposed technique can ...
Discrete nonnegativity for nonlinear cooperative parabolic PDE systems with non-monotone coupling
Discrete nonnegativity principles are established for finite element approximations of nonlinear parabolic PDE systems with mixed boundary conditions. Previous results of the authors are extended such that diagonal dominance ...
On continuous and discrete maximum principles for elliptic problems with the third boundary condition
In this work, we present and discuss some continuous and discrete maximum principles for linear elliptic problems of the second order with the third boundary condition (almost never addressed to in the available literature ...
On modifications of continuous and discrete maximum principles for reaction-diffusion problems
In this work, we present and discuss some modifications, in the form of two-sided estimation (and also for arbitrary source functions instead of usual sign-conditions), of continuous and discrete maximum principles for the ...
Nonobtuse local tetrahedral refinements towards a polygonal face/interface
In this note we show how to generate and conformally refine nonobtuse tetrahedral meshes locally in the neighbourhood of a polygonal face or a polygonal interior interface of a three-dimensional domain. The technique ...
A Geometric Toolbox for Tetrahedral Finite Element Partitions
In this work we present a survey of some geometric results on tetrahedral partitions and their refinements in a unified manner. They can be used for mesh generation and adaptivity in practical calculations by the finite ...