Finite volume approximation of nonlinear agglomeration population balance equation on triangular grid

The Finite Element Approximation of the Nonlinear Poisson-Boltzmann Equation

A widely used electrostatics model in the biomolecular modeling community, the nonlinear Poisson–Boltzmann equation, along with its finite element approximation, are analyzed in this paper. A regularized Poisson–Boltzmann equation is introduced as an auxiliary problem, making it possible to study the original nonlinear equation with delta distribution sources. A priori error estimates for the f...

The Control-Volume Finite-Difference Approximation to the Diffusion Equation

A two-dimensional computer code for solution of the diffusion equation (Poisson equation) is described. The code is implemented in Matlab, and is intended for educational use. The partial differential equation is converted to a system of linear equations with the finite-volume method. The system is solved by a direct method, though extending the code to use iterative methods would not be diffic...

Finite element approximation of a nonlinear cross-diffusion population model

where j = i and gi(u1, u2) := (μi − γii ui − γij uj) ui. In the above, the given data is as follows: v is an environmental potential, c i ∈ R≥0, ai ∈ R>0 are diffusion coefficients, bi ∈ R are transport coefficients, μi ∈ R≥0 are the intrinsic growth rates, and γii ∈ R≥0 are intra-specific, whereas γij , i = j, ∈ R≥0 are interspecific competition coefficients. In addition to showing well-posedn...

Unstructured Volume - Agglomeration MG : Solution of the Poisson Equation

Nonlinear approximation theory on finite groups

Motivated by problems in signal recovery, we will investigate the distribution of the energy of the Fourier transform of a positive function on a finite group. In particular, we are able to bound from below the fraction of energy contained in various subsets of the Fourier transform of a positive function defined on a finite group. Applications to signal recovery for positive functions, as well...