Now showing items 1-10 of 20
A posteriori error analysis of a stabilized mixed FEM for convectuion-diffusion problems
We present an augmented dual-mixed variational formulation for a linear convection-diffusion equation with homogeneous Dirichlet boundary conditions. The approach is based on the addition of suitable least squares type ...
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 nonobtuse refinements of tetrahedral finite element meshes
It is known that piecewise linear continuous finite element (FE) approximations on nonobtuse tetrahedral FE meshes guarantee the validity of discrete analogues of various maximum principles for a wide class of elliptic ...
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 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 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 ...