scholarly journals Finite Difference, Finite Element and Finite Volume Methods for Partial Differential Equations

2005 ◽  
pp. 2415-2446 ◽  
Author(s):  
Joaquim Peiró ◽  
Spencer Sherwin
Keyword(s):  
Finite Element ◽  
Partial Differential Equations ◽  
Finite Difference ◽  
Differential Equations ◽  
Finite Volume ◽  
Finite Volume Methods ◽  
Partial Differential

Solution of some Engineering Partial Differential Equations Governed by the Minimal of a Functional by Global Optimization Method

2013 ◽  
Vol 29 (3) ◽  
pp. 507-516 ◽  
Author(s):  
Y. M. Cheng ◽  
D. Z. Li ◽  
N. Li ◽  
Y. Y Lee ◽  
S. K. Au
Keyword(s):  
Finite Element ◽  
Global Optimization ◽  
Approximate Solution ◽  
Partial Differential Equations ◽  
Finite Difference ◽  
Differential Equations ◽  
Optimization Method ◽  
Global Optimization Method ◽  
Partial Differential ◽  
Special Cases

AbstractMany engineering problems are governed by partial differential equations which can be solved by analytical as well as numerical methods, and examples include the plasticity problem of a geotechnical system, seepage problem and elasticity problem. Although the governing differential equations can be solved by either iterative finite difference method or finite element, there are however limitations to these methods in some special cases which will be discussed in the present paper. The solutions of these governing differential equations can all be viewed as the stationary value of a functional. Using an approximate solution as the initial solution, the stationary value of the functional can be obtained easily by modern global optimization method. Through the comparisons between analytical solutions and fine mesh finite element analysis, the use of global optimization method will be demonstrated to be equivalent to the solutions of the governing partial differential equations. The use of global optimization method can be an alternative to the finite difference/ finite element method in solving an engineering problem, and it is particularly attractive when an approximate solution is available or can be estimated easily.

scholarly journals Haar Wavelet Implementation to Various Partial Differential Equations

2017 ◽  
Vol 2 (3) ◽  
pp. 44
Author(s):  
K. P. Mredula ◽  
D. C. Vakaskar
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Partial Differential Equations ◽  
Finite Difference ◽  
Differential Equations ◽  
Haar Wavelet ◽  
Partial Differential ◽  
Salient Features ◽  
Element Method

The article brings together a series of algorithms with the modification in formulation of solution to various partial differential equations. The algorithms are modified with implementation of Haar Wavelet. Test examples are considered for validation with few cases. Salient features of multi resolution is closely compared with different resolutions. The approach combines well known finite difference and finite element method with wavelets. A detailed description of algorithm is attempted for simplification of the approach.

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