The paper presents analysis of a solution of Laplace equation with the use of FEM harmonic basic functions. The essence of the problem is aimed at presenting an approximate solution based on possibly large finite elem...The paper presents analysis of a solution of Laplace equation with the use of FEM harmonic basic functions. The essence of the problem is aimed at presenting an approximate solution based on possibly large finite element. Introduction of harmonic functions allows to reduce the order of numerical integration as compared to a classical Finite Element Method. Numerical calculations conform good efficiency of the use of basic harmonic functions for resolving direct and inverse problems of stationary heat conduction.Further part of the paper shows the use of basic harmonic functions for solving Poisson’s equation and for drawing up a complete system of biharmonic and polyharmonic basic展开更多
The work presents the application of heat polynomials for solving an inverse problem. The heat polynomials form the Treffetz Method for non-stationary heat conduction problem. They have been used as base functions in ...The work presents the application of heat polynomials for solving an inverse problem. The heat polynomials form the Treffetz Method for non-stationary heat conduction problem. They have been used as base functions in Finite Element Method. Application of heat polynomials permits to reduce the order of numerical integration as compared to the classical Finite Element Method with formulation of the matrix of system of equations.展开更多
基金This work has been partially carried out within the Grant KBN 8T10B06820.
文摘The paper presents analysis of a solution of Laplace equation with the use of FEM harmonic basic functions. The essence of the problem is aimed at presenting an approximate solution based on possibly large finite element. Introduction of harmonic functions allows to reduce the order of numerical integration as compared to a classical Finite Element Method. Numerical calculations conform good efficiency of the use of basic harmonic functions for resolving direct and inverse problems of stationary heat conduction.Further part of the paper shows the use of basic harmonic functions for solving Poisson’s equation and for drawing up a complete system of biharmonic and polyharmonic basic
基金The present work is an effect of work within KBN 8T10B01913 Grant cooperation with the Chair of Steam-Gas Turbines of TU Dresden supported by the Humboldt-Foundation.
文摘The work presents the application of heat polynomials for solving an inverse problem. The heat polynomials form the Treffetz Method for non-stationary heat conduction problem. They have been used as base functions in Finite Element Method. Application of heat polynomials permits to reduce the order of numerical integration as compared to the classical Finite Element Method with formulation of the matrix of system of equations.
