Numerical investigation of convergence in the $ L^{\infty} $ norm for modified SGFEM applied to elliptic interface problems

Convergence in the $ L^{\infty} $ norm is a very important consideration in numerical simulations of interface problems. In this paper, a modified stable generalized finite element method (SGFEM) was proposed for solving the second-order elliptic interface problem in the two-dimensional bounded and...

Celý popis

Uloženo v:

Podrobná bibliografie
Vydáno v:	AIMS mathematics Ročník 9; číslo 11; s. 31252 - 31273
Hlavní autoři:	Zhu, Pengfei, Liu, Kai
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	AIMS Press 01.01.2024
Témata:	convergence elliptic interface problem l^{\infty} $ norm scaled condition number sgfem
ISSN:	2473-6988, 2473-6988
On-line přístup:	Získat plný text
Tagy:	Přidat tag Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!

Popis
Shrnutí:	Convergence in the $ L^{\infty} $ norm is a very important consideration in numerical simulations of interface problems. In this paper, a modified stable generalized finite element method (SGFEM) was proposed for solving the second-order elliptic interface problem in the two-dimensional bounded and convex domain. The proposed SGFEM uses a one-side enrichment function. There is no stability term in the weak form of the model problem, and it is a conforming finite element method. Moreover, it is applicable to any smooth interface, regardless of its concavity or shape. Several nontrivial examples illustrate the excellent properties of the proposed SGFEM, including its convergence in both the $ L^2 $ and $ L^{\infty} $ norms, as well as its stability and robustness.
ISSN:	2473-6988 2473-6988
DOI:	10.3934/math.20241507