0000000000255668

AUTHOR

Sergey Korotov

showing 4 related works from this author

Weakened acute type condition for tetrahedral triangulations and the discrete maximum principle

2000

We prove that a discrete maximum principle holds for continuous piecewise linear finite element approximations for the Poisson equation with the Dirichlet boundary condition also under a condition of the existence of some obtuse internal angles between faces of terahedra of triangulations of a given space domain. This result represents a weakened form of the acute type condition for the three-dimensional case.

Dirichlet problemAlgebra and Number TheoryDiscretizationApplied MathematicsMathematical analysisDomain (mathematical analysis)Piecewise linear functionComputational Mathematicssymbols.namesakeMaximum principleDirichlet boundary conditionsymbolsBoundary value problemPoisson's equationMathematicsMathematics of Computation
researchProduct

Discrete Maximum Principle for Galerkin Finite Element Solutions to Parabolic Problems on Rectangular Meshes

2004

One of the most important problems in numerical simulation is the preservation of qualitative properties of solutions of mathematical models. For problems of parabolic type, one of such properties is the maximum principle. In [5], Fujii analyzed the discrete analogue of the (continuous) maximum principle for the linear parabolic problems, and derived sufficient conditions guaranteeing its validity for the Galerkin finite element approximations built on simplicial meshes. In our paper, we present the sufficient conditions for the validity of the discrete maximum principle for the case of bilinear finite element space approximations on rectangular meshes.

Maximum principleComputer simulationMathematical modelDiscontinuous Galerkin methodBilinear interpolationApplied mathematicsPolygon meshGalerkin methodFinite element methodMathematics
researchProduct

Acute Type Refinements of Tetrahedral Partitions of Polyhedral Domains

2001

We present a new technique to perform refinements on acute type tetrahedral partitions of a polyhedral domain, provided that the center of the circumscribed sphere around each tetrahedron belongs to the tetrahedron. The resulting family of partitions is of acute type; thus, all the tetrahedra satisfy the maximum angle condition. Both these properties are highly desirable in finite element analysis.

Numerical AnalysisApplied MathematicsDomain decomposition methodsAngle conditionFinite element methodCombinatoricsComputational MathematicsPolyhedronMaximum principleTetrahedronMathematics::Metric GeometryPartition (number theory)Circumscribed sphereMathematicsSIAM Journal on Numerical Analysis
researchProduct

Finite element analysis of varitional crimes for a quasilinear elliptic problem in 3D

2000

We examine a finite element approximation of a quasilinear boundary value elliptic problem in a three-dimensional bounded convex domain with a smooth boundary. The domain is approximated by a polyhedron and a numerical integration is taken into account. We apply linear tetrahedral finite elements and prove the convergence of approximate solutions on polyhedral domains in the $W^1_2$ -norm to the true solution without any additional regularity assumptions.

Computational MathematicsElliptic curvePolyhedronApplied MathematicsNumerical analysisNorm (mathematics)Bounded functionMathematical analysisBoundary value problemFinite element methodNumerical integrationMathematicsNumerische Mathematik
researchProduct