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The combination technique for a two-dimensional convection-diffusion problem with exponential layers

Sebastian Franz, Fang Liu, Hans-Görg Roos, Martin Stynes, Aihui Zhou (2009)

Applications of Mathematics

Convection-diffusion problems posed on the unit square and with solutions displaying exponential layers are solved using a sparse grid Galerkin finite element method with Shishkin meshes. Writing $N$ for the maximum number of mesh intervals in each coordinate direction, our “combination” method simply adds or subtracts solutions that have been computed by the Galerkin FEM on $N \times \sqrt{N}$ , $\sqrt{N} \times N$ and $\sqrt{N} \times \sqrt{N}$ meshes. It is shown that the combination FEM yields (up to a factor $ln N$ ) the same order of accuracy in the associated...

The Contraction Number of a Multigrid Method for Solving the Poisson Equation.

D. Braess (1981)

Numerische Mathematik

The convergence of a new method for calculating lower bounds to eigenvalues

Goerisch, Friedrich, Albrecht, Julius (1986)

Equadiff 6

The Convergence of Inexact Chebyshev and Richardson Iterative Methods for Solving Linear Systems.

Gene H. Golub, Michael L. Overton (1988)

Numerische Mathematik

The Convergence of the Method of Conjugate Gradients at Isolated Extreme Points of the Spectrum.

G.W. Stewart (1975)

Numerische Mathematik

The Convergence rate and Complexity of Precondotioned Iterative methods based on Approximate finite Element matrix Factorization

Elias A. Lipitakis, George A. Gravvanis (1992)

Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

The convergence rate of the Chebyshev semiiterative method under a perturbation of the foci of an elliptic domain.

Li, Xiezhang, Arroyo, Fangjun (2002)

ELA. The Electronic Journal of Linear Algebra [electronic only]

The Coordinex Problem and Its Relation to the Conjecture of Wilkinson.

H. Puschmann, J. Cortés (1983)

Numerische Mathematik

The $D$ -stability problem for $4 \times 4$ real matrices

Serkan T. Impram, Russell Johnson, Raffaella Pavani (2005)

Archivum Mathematicum

We give detailed discussion of a procedure for determining the robust $D$ -stability of a $4 \times 4$ real matrix. The procedure begins from the Hurwitz stability criterion. The procedure is applied to two numerical examples.

The descent algorithms for solving symmetric Pareto eigenvalue complementarity problem

Lu Zou, Yuan Lei (2023)

Applications of Mathematics

For the symmetric Pareto Eigenvalue Complementarity Problem (EiCP), by reformulating it as a constrained optimization problem on a differentiable Rayleigh quotient function, we present a class of descent methods and prove their convergence. The main features include: using nonlinear complementarity functions (NCP functions) and Rayleigh quotient gradient as the descent direction, and determining the step size with exact linear search. In addition, these algorithms are further extended to solve the...