Weak-element Approximations to Elliptic Differential Equations.
Weighted inequalities for gradients on non-smooth domains [Book]
Weighted Miranda-Talenti inequality and applications to equations with discontinuous coefficients
Let be an open bounded set in , with boundary, and (, ) be a weighted Morrey space. In this note we prove a weighted version of the Miranda-Talenti...
Well-posedness of the Dirichlet problem and homotopy classification of elliptic systems of second-order partial differential equations
What is the smallest possible constant in Céa's lemma?
We consider finite element approximations of a second order elliptic problem on a bounded polytopic domain in with . The constant appearing in Céa’s lemma and coming from its standard proof can be very large when the coefficients of an elliptic operator attain considerably different values. We restrict ourselves to regular families of uniform partitions and linear simplicial elements. Using a lower bound of the interpolation error and the supercloseness between the finite element solution and...
Which sequences of holes are admissible for periodic homogenization with Neumann boundary condition?
In this paper we give a general presentation of the homogenization of Neumann type problems in periodically perforated domains, including the case where the shape of the reference hole varies with the size of the period (in the spirit of the construction of self-similar fractals). We shows that -convergence holds under the extra assumption that there exists a bounded sequence of extension operators for the reference holes. The general class of Jones-domains gives an example where this result applies....
Which sequences of holes are admissible for periodic homogenization with Neumann boundary condition?
In this paper we give a general presentation of the homogenization of Neumann type problems in periodically perforated domains, including the case where the shape of the reference hole varies with the size of the period (in the spirit of the construction of self-similar fractals). We shows that H0-convergence holds under the extra assumption that there exists a bounded sequence of extension operators for the reference holes. The general class of Jones-domains gives an example where this result...
Which solutions of the third problem for the Poisson equation are bounded?
Wiener's test of thinness in potential theory
Worst scenario method in homogenization. Linear case
The paper deals with homogenization of a linear elliptic boundary problem with a specific class of uncertain coefficients describing composite materials with periodic structure. Instead of stochastic approach to the problem, we use the worst scenario method due to Hlaváček (method of reliable solution). A few criterion functionals are introduced. We focus on the range of the homogenized coefficients from knowledge of the ranges of individual components in the composite, on the values of generalized...
Zienkiewicz–Zhu error estimators on anisotropic tetrahedral and triangular finite element meshes
We consider a posteriori error estimators that can be applied to anisotropic tetrahedral finite element meshes, i.e. meshes where the aspect ratio of the elements can be arbitrarily large. Two kinds of Zienkiewicz–Zhu (ZZ) type error estimators are derived which originate from different backgrounds. In the course of the analysis, the first estimator turns out to be a special case of the second one, and both estimators can be expressed using some recovered gradient. The advantage of keeping two different...
Zienkiewicz–Zhu error estimators on anisotropic tetrahedral and triangular finite element meshes
We consider a posteriori error estimators that can be applied to anisotropic tetrahedral finite element meshes, i.e. meshes where the aspect ratio of the elements can be arbitrarily large. Two kinds of Zienkiewicz–Zhu (ZZ) type error estimators are derived which originate from different backgrounds. In the course of the analysis, the first estimator turns out to be a special case of the second one, and both estimators can be expressed using some recovered gradient. The advantage of keeping two...
Zur Konvergenz des Peaceman-Rachford-Verfahrens. -On the Convergence of the Peaceman-Rachford Iterative Method.
Алгоритм блуждания по параллелепипедам для решения краевой задачи для дифференциального уравнения эллптического типа
Аналитическое продолжение по параметру функций Грина внешних краевых задач для двумерного уравнения Гельмгольца. III
Априорная оценка oeoeuoeoe выпуклых решений задачи Дирихле для уравнения Монжа-Ампера
Асимптотика емкости конденсатора с пластинами произвольной формы.
Асимптотика решения задачи Дирихле для уравнения с быстро осциллирующими коэффициентами в прямоугольнике
Асимптотика спектральной функции эллиптического дифференциального оператор второго порядка
Асимптотическое поведение решений эллиптических уравнений второго порядка вблизи границы. II