Scholarlink

Abstract <p>A new additive representation has been obtained for solving an elliptic problem with a point source, explicitly isolating the singularity caused by the presence of the source. A problem for the unknown component of the decomposition is formulated, and the smoothness of its solution is established, namely, its membership in the Sobolev space <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(W_{2}^{{(2)}}\)</EquationSource> <!--RusMath2670019Trifonova-m1--> </InlineEquation>. The proposed representation allows the use of standard numerical methods without mesh refinement for solving equations with point sources.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Regularity of the Components in the Additive Representation of the Solution to an Elliptic Boundary Value Problem with a Point Source

  • 期刊论文

  • 发表日期：

    2026年2月1日

查看全文
  • G. O. Trifonova

摘要

Abstract

A new additive representation has been obtained for solving an elliptic problem with a point source, explicitly isolating the singularity caused by the presence of the source. A problem for the unknown component of the decomposition is formulated, and the smoothness of its solution is established, namely, its membership in the Sobolev space \(W_{2}^{{(2)}}\) . The proposed representation allows the use of standard numerical methods without mesh refinement for solving equations with point sources.