Now showing items 1-10 of 10
Some discrete maximum principles arising for nonlinear elliptic finite element problems
The discrete maximum principle (DMP) is an important measure of the qualitative reliability of the applied numerical scheme for elliptic problems. This paper starts with formulating simple sufficient conditions for the ...
On the maximum angle condition for the conforming longest-edge n-section algorithm for large values of n
In this note we introduce the conforming longest-edge $n$-section algorithm and show that for $n \ge 4$ it produces a family of triangulations which does not satisfy the maximum angle condition.
On numerical regularity of the face-to-face longest-edge bisection algorithm for tetrahedral partitions
The finite element method usually requires regular or strongly regular families of partitions in order to get guaranteed a priori or a posteriori error estimates. In this paper we examine the recently invented longest-edge ...
Red refinements of simplices into congruent subsimplices
We show that in dimensions higher than two, the popular "red refinement" technique, commonly used for simplicial mesh refinements and adaptivity in the finite element analysis and practice, never yields subsimplices which ...
On Conforming Tetrahedralisations of Prismatic Partitions
We present an algorithm for conform (face-to-face) subdividing prismatic partitions into tetrahedra. This algorithm can be used in the finite element calculations and analysis.
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 ...
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 ...
On global and local mesh refinements by a generalized conforming bisection algorithm
We examine a generalized conforming bisection (GCB-)algorithm which allows both global and local nested refinements of the triangulations without generating hanging nodes. It is based on the notion of a mesh density function ...