Postprocessing Galerkin method using quadratic spline wavelets and its efficiency

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F46747885%3A24510%2F18%3A00004635" target="_blank" >RIV/46747885:24510/18:00004635 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0898122118300567" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0898122118300567</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.camwa.2018.01.040" target="_blank" >10.1016/j.camwa.2018.01.040</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Postprocessing Galerkin method using quadratic spline wavelets and its efficiency

Popis výsledku v původním jazyce

The wavelet-Galerkin method is a useful tool for solving differential equations mainly because the condition number of the stiffness matrix is independent of the matrix size and thus the number of iterations for solving the discrete problem by the conjugate gradient method is small. We have recently proposed a quadratic spline wavelet basis that has a small condition number and a short support. In this paper we use this basis in the Galerkin method for solving the second-order elliptic problems with Dirichlet boundary conditions in one and two dimensions and by an appropriate post-processing we achieve the L2-error of order O(h^4) and the H1-error of order (h^3), where his the step size. The rate of convergence is the same as the rate of convergence for the Galerkin method with cubic spline wavelets. We show theoretically as well as numerically that the presented method outperforms the Galerkin method with other quadratic or cubic spline wavelets. Furthermore, we present local post-processing for example of the equation with Dirac measure on the right-hand side.

Název v anglickém jazyce

Postprocessing Galerkin method using quadratic spline wavelets and its efficiency

Popis výsledku anglicky

The wavelet-Galerkin method is a useful tool for solving differential equations mainly because the condition number of the stiffness matrix is independent of the matrix size and thus the number of iterations for solving the discrete problem by the conjugate gradient method is small. We have recently proposed a quadratic spline wavelet basis that has a small condition number and a short support. In this paper we use this basis in the Galerkin method for solving the second-order elliptic problems with Dirichlet boundary conditions in one and two dimensions and by an appropriate post-processing we achieve the L2-error of order O(h^4) and the H1-error of order (h^3), where his the step size. The rate of convergence is the same as the rate of convergence for the Galerkin method with cubic spline wavelets. We show theoretically as well as numerically that the presented method outperforms the Galerkin method with other quadratic or cubic spline wavelets. Furthermore, we present local post-processing for example of the equation with Dirac measure on the right-hand side.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA16-09541S" target="_blank" >GA16-09541S: Robustní numerická schémata pro oceňování vybraných opcí za různých tržních podmínek</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Computers & Mathematics with Applications

ISSN

0898-1221

e-ISSN

—

Svazek periodika

75

Číslo periodika v rámci svazku

9

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

15

Strana od-do

3186-3200

Kód UT WoS článku

000432102900009

EID výsledku v databázi Scopus

2-s2.0-85042033830