Now showing items 1-20 of 21

• #### Discrete maximum principles for nonlinear parabolic PDE systems ﻿

(2012-12-31)
Discrete maximum principles (DMPs) are established for finite element approximations of systems of nonlinear parabolic partial differential equations with mixed boundary and interface conditions. The results are based on ...
• #### Discrete nonnegativity for nonlinear cooperative parabolic PDE systems with non-monotone coupling ﻿

(2013-12-31)
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 ...
• #### Editors' preface for the topical issue "Advances in Numerical Analysis and Numerical Linear Algebra" ﻿

(2012-12-31)
[No abstract available]
• #### Editors' preface for the topical issue "Numerical Methods for Large-Scale Scientific Computing, I" ﻿

(2013-12-31)
[No abstract available]
• #### Editors' preface for the topical issue "Numerical Methods for Large-Scale Scientific Computing, II" ﻿

(2013-12-31)
[No abstract available]
• #### Generalization of the Zlámal condition for simplicial finite elements in ℝ d ﻿

(2011-12-31)
The famous Zlámal's minimum angle condition has been widely used for construction of a regular family of triangulations (containing nondegenerating triangles) as well as in convergence proofs for the finite element method ...
• #### A Geometric Toolbox for Tetrahedral Finite Element Partitions ﻿

(2011-12-31)
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 ...
• #### Local nonobtuse tetrahedral refinements around an edge ﻿

(2013-12-31)
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 ...
• #### The maximum angle condition is not necessary for convergence of the finite element method ﻿

(2012-12-31)
We show that the famous maximum angle condition in the finite element analysis is not necessary to achieve the optimal convergence rate when simplicial finite elements are used to solve elliptic problems. This condition ...
• #### Nonobtuse local tetrahedral refinements towards a polygonal face/interface ﻿

(2011-12-31)
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 ...
• #### On Conforming Tetrahedralisations of Prismatic Partitions ﻿

(2013-12-31)
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.
• #### On continuous and discrete maximum principles for elliptic problems with the third boundary condition ﻿

(2013-12-31)
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 global and local mesh refinements by a generalized conforming bisection algorithm ﻿

(2010-12-31)
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 ...
• #### On modifications of continuous and discrete maximum principles for reaction-diffusion problems ﻿

(2011-12-31)
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 ...
• #### On nonobtuse refinements of tetrahedral finite element meshes ﻿

(2014-12-31)
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 ﻿

(2014-12-31)
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 ...
• #### On the maximum angle condition for the conforming longest-edge n-section algorithm for large values of n ﻿

(2015-12-31)
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.
• #### A posteriori error analysis of a stabilized mixed FEM for convectuion-diffusion problems ﻿

(2015-12-31)
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 ...
• #### Radiation of water waves by a submerged nearly circular plate ﻿

(2016-01-01)
A thin nearly circular plate is submerged below the free surface of deep water. The problem is reduced to a hypersingular integral equation over the surface of the plate which is conformally mapped onto the unit disc. The ...
• #### Red refinements of simplices into congruent subsimplices ﻿

(2014-12-31)
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 ...