Existence, Uniqueness, and a Comparison of Nonintrusive Methods for the Stochastic Nonlinear Poisson--Boltzmann Equation

Numerical optimization and variational techniques (65K10) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

Uses Software

TOMS659

Cites Work

Unnamed Item
Unnamed Item
Unnamed Item
Boundedness of stable solutions to semilinear elliptic equations: a survey
Sparse pseudospectral approximation method
Multiscale modeling of fluctuations in stochastic elliptic PDE models of nanosensors
Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations
An asymptotic-preserving stochastic Galerkin method for the radiative heat transfer equations with random inputs and diffusive scalings
The complexity of linear tensor product problems in (anti)symmetric Hilbert spaces
Finite elements for elliptic problems with stochastic coefficients
Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos
Analytic regularity and nonlinear approximation of a class of parametric semilinear elliptic PDEs
Approximation of Quantities of Interest in Stochastic PDEs by the Random Discrete $L^2$ Projection on Polynomial Spaces
Analytic Regularity and GPC Approximation for Control Problems Constrained by Linear Parametric Elliptic and Parabolic PDEs
ANALYTIC REGULARITY AND POLYNOMIAL APPROXIMATION OF PARAMETRIC AND STOCHASTIC ELLIPTIC PDE'S
Stochastic finite elements: Computational approaches to stochastic partial differential equations
Algorithm 659
Elliptic Partial Differential Equations of Second Order
Cubature Formulas for Multisymmetric Functions and Applications to Stochastic Partial Differential Equations
Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
To Be or Not to Be Intrusive? The Solution of Parametric and Stochastic Equations---the “Plain Vanilla” Galerkin Case
To Be or Not to be Intrusive? The Solution of Parametric and Stochastic Equations---Proper Generalized Decomposition
An Asymptotic-Preserving Stochastic Galerkin Method for the Semiconductor Boltzmann Equation with Random Inputs and Diffusive Scalings
A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
Direct methods in the calculus of variations

This page was built for publication: Existence, Uniqueness, and a Comparison of Nonintrusive Methods for the Stochastic Nonlinear Poisson--Boltzmann Equation