A diffusion reaction system modelling spatial patterns
A direct solver for finite element matrices requiring memory places
We present a method that in certain sense stores the inverse of the stiffness matrix in memory places, where is the number of degrees of freedom and hence the matrix size. The setup of this storage format requires arithmetic operations. However, once the setup is done, the multiplication of the inverse matrix and a vector can be performed with operations. This approach applies to the first order finite element discretization of linear elliptic and parabolic problems in triangular domains,...
A duality principle for delay equations
A finite element method for a model of population dynamics with spatial diffusion
A finite element method for the computation of parametric minimal surfaces
A forced quasilinear wave equation with dissipation
A method to rigorously enclose eigenpairs of complex interval matrices
In this paper, a rigorous computational method to enclose eigenpairs of complex interval matrices is proposed. Each eigenpair is found by solving a nonlinear equation of the form via a contraction argument. The set-up of the method relies on the notion of , which provide an efficient mean of determining a domain on which the contraction mapping theorem is applicable.
A model for phenomena of instability
A new description and some modifications of Filippov cone
A new iterative algorithm for solving the fictitious fluxes method problems for elliptic equations
A new view of center manifolds
A note on symmetries of invariant sets with compact group actions
A parallel method for population balance equations based on the method of characteristics
In this paper, we present a parallel scheme to solve the population balance equations based on the method of characteristics and the finite element discretization. The application of the method of characteristics transform the higher dimensional population balance equation into a series of lower dimensional convection-diffusion-reaction equations which can be solved in a parallel way. Some numerical results are presented to show the accuracy and efficiency.
A partially ordered space connected with the de la Vallée Poussin problem
A priori bounds for a semilinear wave equation
A short philosophical note on the origin of smoothed aggregations
We derive the smoothed aggregation two-level method from the variational objective to minimize the final error after finishing the entire iteration. This contrasts to a standard variational two-level method, where the coarse-grid correction vector is chosen to minimize the error after coarse-grid correction procedure, which represents merely an intermediate stage of computing. Thus, we enforce the global minimization of the error. The method with smoothed prolongator is thus interpreted as a qualitatively...
-stability and numerical solution of abstract differential equations
A tribute to Bernard Bolzano
About the representation of solutions of linear elliptic equations of arbitrary order
Abstract Cauchy problem