FINITE ELEMENT METHODS FOR SEMILINEAR ELLIPTIC PROBLEMS WITH SMOOTH INTERFACES

被引：1

作者：

Deka, Bhupen ^{[1
]}

Ahmed, Tazuddin ^{[1
]}

机构：

[1] Tezpur Univ, Dept Math Sci, Tezpur 784028, Assam, India

来源：

INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS | 2011年 / 42卷 / 04期

关键词：

Elliptic; interface; semilinear; finite element method; optimal error estimate;

D O I：

10.1007/s13226-011-0014-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The purpose of this paper is to study the finite element method for second order semilinear elliptic interface problems in two dimensional convex polygonal domains. Due to low global regularity of the solution, it seems difficult to achieve optimal order of convergence with straight interface triangles [Numer Math., 79 (1998), pp. 175-202]. For a finite element discretization based on a mesh which involve the approximation of the interface, optimal order error estimates in L(2) and H(1)-norms are proved for linear elliptic interface problem under practical regularity assumptions of the true solution. Then an extension to the semilinear problem is also considered and optimal error estimate in H(1) norm is achieved.

引用

页码：205 / 223

页数：19

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