Search results for "dirichlet"
showing 7 items of 197 documents
A Domain Imbedding Method with Distributed Lagrange Multipliers for Acoustic Scattering Problems
2003
The numerical computation of acoustic scattering by bounded twodimensional obstacles is considered. A domain imbedding method with Lagrange multipliers is introduced for the solution of the Helmholtz equation with a second-order absorbing boundary condition. Distributed Lagrange multipliers are used to enforce the Dirichlet boundary condition on the scatterer. The saddle-point problem arising from the conforming finite element discretization is iteratively solved by the GMRES method with a block triangular preconditioner. Numerical experiments are performed with a disc and a semi-open cavity as scatterers.
Poincare Inequalities and Spectral Gap, Concentration Phenomenon for G-Measures
2002
We produce a new approach based upon inequalities of Poincare’s type for giving constructive estimates of the mixing rate for a family of mixing stationary processes continuously depending on their past called g-measures. We establish also exponential inequalities of Hoeffding’s type leading to a concentration phenomenon for a large class of observables; this last property permits in particular to give the typical behaviour of the n-orbits of a g-measure.
A Fixed Domain Approach in Shape Optimization Problems with Neumann Boundary Conditions
2008
Fixed domain methods have well-known advantages in the solution of variable domain problems, but are mainly applied in the case of Dirichlet boundary conditions. This paper examines a way to extend this class of methods to the more difficult case of Neumann boundary conditions.
Isometries between spaces of multiple Dirichlet series
2019
Abstract In this paper we study spaces of multiple Dirichlet series and their properties. We set the ground of the theory of multiple Dirichlet series and define the spaces H ∞ ( C + k ) , k ∈ N , of convergent and bounded multiple Dirichlet series on C + k . We give a representation for these Banach spaces and prove that they are all isometrically isomorphic, independently of the dimension. The analogous result for A ( C + k ) , k ∈ N , which are the spaces of multiple Dirichlet series that are convergent on C + k and define uniformly continuous functions, is obtained.
Errors Generated by Uncertain Data
2014
In this chapter, we study effects caused by incompletely known data. In practice, the data are never known exactly, therefore the results generated by a mathematical model also have a limited accuracy. Then, the whole subject of error analysis should be treated in a different manner, and accuracy of numerical solutions should be considered within a framework of a more complicated scheme, which includes such notions as maximal and minimal distances to the solution set and its radius.
A posteriori error estimates for time-dependent reaction-diffusion problems based on the Payne-Weinberger inequality
2015
We consider evolutionary reaction-diffusion problem with mixed Dirichlet--Robin boundary conditions. For this class of problems, we derive two-sided estimates of the distance between any function in the admissible energy space and exact solution of the problem. The estimates (majorants and minorants) are explicitly computable and do not contain unknown functions or constants. Moreover, it is proved that the estimates are equivalent to the energy norm of the deviation from the exact solution.
Stokastinen reunasäännöllisyys ja häiritty köydenvetopeli
2014
Tämän tutkielman tarkoituksena on tutkia Dirichlet'n ongelmaa todennäköisyysteorian ja peliteorian näkökulmasta. Osoittautuu, että käytössä olevan alueen reuna vaikuttaa siihen, onko olemassa Dirichlet'n ongelman ratkaisevaa funktiota, joka saavuttaa oikeat reuna-arvot jatkuvasti. Tutkielmassa määritellään joukon reunasäännöllisyys jatkuva-aikaisen satunnaisliikkeen avulla. Käyttökelpoinen ja riittävä ehto reunapisteen säännöllisyydelle on Poincarén kartioehto. Tässä työssä näytetään myös Wienerin kriteerio, joka on riittävä ja välttämätön ehto reunapisteen säännöllisyydelle. Tutkielmassa käsitellään myös p-Laplacen yhtälöä käyttäen apuna häirittyä köydenvetopeliä (tug-of-war with noise). H…