Weak truncation error estimates for elliptic PDEs with lognormal coefficients
نویسندگان
چکیده
منابع مشابه
Strong and weak error estimates for the solutions of elliptic partial differential equations with random coefficients
We consider the problem of numerically approximating the solution of an elliptic partial di erential equation with random coe cients and homogeneous Dirichlet boundary conditions. We focus on the case of a lognormal coe cient, we have then to deal with the lack of uniform coercivity and uniform boundedness with respect to the randomness. This model is frequently used in hydrogeology. We approxi...
متن کاملQuasi-Monte Carlo finite element methods for elliptic PDEs with lognormal random coefficients
In this paper we analyze the numerical approximation of diffusion problems over polyhedral domains in R (d = 1, 2, 3), with diffusion coefficient a(x, ω) given as a lognormal random field, i.e., a(x, ω) = exp(Z(x, ω)) where x is the spatial variable and Z(x, ·) is a Gaussian random field. The analysis presents particular challenges since the corresponding bilinear form is not uniformly bounded ...
متن کاملSparse polynomial approximation of parametric elliptic PDEs Part II: lognormal coefficients *
We consider the linear elliptic equation −div(a∇u) = f on some bounded domain D, where a has the form a = exp(b) with b a random function defined as b(y) = ∑ j≥1 yjψj where y = (yj) ∈ RN are i.i.d. standard scalar Gaussian variables and (ψj)j≥1 is a given sequence of functions in L∞(D). We study the summability properties of Hermite-type expansions of the solution map y 7→ u(y) ∈ V := H 0 (D), ...
متن کاملElliptic regularity and solvability for PDEs with Colombeau coefficients
The paper addresses questions of existence and regularity of solutions to linear partial differential equations whose coefficients are generalized functions or generalized constants in the sense of Colombeau. We introduce various new notions of ellipticity and hypoellipticity, study their interrelation, and give a number of new examples and counterexamples. Using the concept of G∞-regularity of...
متن کاملOn Finite Element Error Estimates for Optimal Control Problems with Elliptic PDEs
Discretizations of optimal control problems for elliptic equations by finite element methods are considered. The problems are subject to constraints on the control and may also contain pointwise state constraints. Some techniques are surveyed to estimate the distance between the exact optimal control and the associated optimal control of the discretized problem. As a particular example, an erro...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Stochastic Partial Differential Equations: Analysis and Computations
سال: 2013
ISSN: 2194-0401,2194-041X
DOI: 10.1007/s40072-013-0006-2