On the solution of the inhomogeneous polyharmonic equation and the inhomogeneous Helmholtz equation

DOI10.1134/S0012266110030080zbMath1194.31007WikidataQ115252554 ScholiaQ115252554MaRDI QIDQ981783

N. A. Antropova, Valery V. Karachik

Publication date: 2 July 2010

Published in: Differential Equations (Search for Journal in Brave)

zbMATH Keywords

Helmholtz equationPoisson equationpolyharmonic equation

Mathematics Subject Classification ID

Biharmonic and polyharmonic equations and functions in higher dimensions (31B30)

Related Items (15)

Arbitrary order Trefftz-like basis functions on polygonal meshes and realization in BEM-based FEM ⋮ Unnamed Item ⋮ Generalized third boundary value problem for the biharmonic equation ⋮ Construction of polynomial solutions to the Dirichlet problem for the polyharmonic equation in a ball ⋮ Unnamed Item ⋮ Solution of the Dirichlet problem with polynomial data for the polyharmonic equation in a ball ⋮ Evaluation of Inner Products of Implicitly Defined Finite Element Functions on Multiply Connected Planar Mesh Cells ⋮ Trefftz Finite Elements on Curvilinear Polygons ⋮ Solvability of nonlocal Dirichlet problem for generalized Helmholtz equation in a unit ball ⋮ Construction of polynomial solutions to the Dirichlet problem by Almansi representation ⋮ Polynomial solutions of the Dirichlet problem for the biharmonic equation in the ball ⋮ A Nyström-based finite element method on polygonal elements ⋮ Residual based error estimate and quasi-interpolation on polygonal meshes for high order BEM-based FEM ⋮ Quadrature for implicitly-defined finite element functions on curvilinear polygons ⋮ Reduction of the Lamé Tensor Equations to the System of Non-Coupled Tetraharmonic Equations

Cites Work

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• Normalized system of functions with respect to the Laplace operator and its applications.
• On an expansion of Almansi type
• On one representation of analytic functions by harmonic functions
• Integral Operators in the Theory of Linear Partial Differential Equations

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