Accurate and efficient numerical solutions for elliptic obstacle problems
نویسندگان
چکیده
منابع مشابه
Accurate and efficient numerical solutions for elliptic obstacle problems
Elliptic obstacle problems are formulated to find either superharmonic solutions or minimal surfaces that lie on or over the obstacles, by incorporating inequality constraints. In order to solve such problems effectively using finite difference (FD) methods, the article investigates simple iterative algorithms based on the successive over-relaxation (SOR) method. It introduces subgrid FD method...
متن کاملDiscrete Monotonicity Principle for Numerical Solutions of Obstacle Problems
A new monotonicity principle and an L stability theorem are es tablished for a discrete obstacle problem which is de ned by a piece wise linear nite element discretization of a continuous problem This discrete monotonicity principle extends the discrete maximum princi ple of Ciarlet from linear equations to obstacle problems As an application of the monotonicity principle and the L stability th...
متن کاملNumerical Methods for Accurate Finite Element Solutions of Elliptic Boundary Value Problems Containing Singularities
The Method of Auxiliary Mapping (MAM), introduced by Babuška and Oh, was proven to be very successful in dealing with monotone singularities arising in two dimensional problems. In this paper, in the framework of the p-version of FEM, MAM is presented for one-dimensional elliptic boundary value problems containing singularities. Moreover, in order to show the effectiveness of MAM, a detailed pr...
متن کاملE ect of numerical integrationfor elliptic obstacle problems ?
An elliptic obstacle problem is approximated by piecewise linear-nite elements with numerical integration on the penalty and forcing terms. This leads to diagonal nonlinearities and thereby to a practical scheme. Optimal error estimates in the maximum norm are derived. The proof is based on constructing suitable super and subsolutions that exploit the special structure of the penal-ization, and...
متن کاملBoundary Regularity of Weak Solutions to Nonlinear Elliptic Obstacle Problems
for all v∈ ={v∈W 0 (Ω), v≥ψ a.e. in Ω}. Here Ω is a bounded domain in RN (N≥2) with Lipschitz boundary, 2≤ p ≤N . A(x,ξ) :Ω×RN → RN satisfies the following conditions: (i) A is a vector valued function, the mapping x → A(x,ξ) is measurable for all ξ ∈ RN , ξ → A(x,ξ) is continuous for a.e. x ∈Ω; (ii) the homogeneity condition: A(x, tξ)= t|t|p−2A(x,ξ), t ∈ R, t = 0; (iii) the monotone inequality...
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: Journal of Inequalities and Applications
سال: 2017
ISSN: 1029-242X
DOI: 10.1186/s13660-017-1309-z