Error estimate of finite element/finite difference technique for solution of two-dimensional weakly singular integro-partial differential equation with space and time fractional derivatives

2019 ◽  
Vol 356 ◽  
pp. 314-328 ◽  
Author(s):  
Mehdi Dehghan ◽  
Mostafa Abbaszadeh
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Finite Element ◽  
Finite Difference ◽  
Error Estimate ◽  
Fractional Derivatives ◽  
Two Dimensional ◽  
Partial Differential ◽  
Finite Difference Technique ◽  
Weakly Singular

Finite Difference, Finite Element and Boundary Element Formulae as a Language of Applied Physics

1991 ◽  
Vol 02 (01) ◽  
pp. 383-386
Author(s):  
JIŘÍ KAFKA ◽  
NGUYEN VAN NHAC
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Finite Element ◽  
Partial Differential Equations ◽  
Finite Difference ◽  
Differential Equations ◽  
Integral Form ◽  
The Other ◽  
Applied Physics ◽  
Partial Differential

When deducing the finite difference formulae, one has to discretize partial differential equations. On the other hand, those equations have been previously derived having started from laws of physics in their integral form. So, a question arises, why not avoid the approach to the limit (necessary to deduce the partial differential equation) and why not deduce the finite difference formulae directly on the base of laws of physics in their integral form.

Adaptive Finite Element Method for Solving Poisson Partial Differential Equation

2021 ◽  
Vol 4 (1) ◽  
pp. 1-18
Author(s):  
Gokul KC ◽  
Ram Prasad Dulal
Keyword(s):  
Differential Equation ◽  
Finite Element Method ◽  
Partial Differential Equation ◽  
Finite Element ◽  
Poisson Equation ◽  
Rectangular Domain ◽  
Adaptive Finite Element Method ◽  
Adaptive Finite Element ◽  
Partial Differential ◽  
Element Method

Poisson equation is an elliptic partial differential equation, a generalization of Laplace equation. Finite element method is a widely used method for numerically solving partial differential equations. Adaptive finite element method distributes more mesh nodes around the area where singularity of the solution happens. In this paper, Poisson equation is solved using finite element method in a rectangular domain with Dirichlet and Neumann boundary conditions. Posteriori error analysis is used to mark the refinement area of the mesh. Dorfler adaptive algorithm is used to refine the marked mesh. The obtained results are compared with exact solutions and displayed graphically.

Explorations and Expectations of Equidistribution Adaptations for Nonlinear Quenching Problems

2013 ◽  
Vol 5 (04) ◽  
pp. 407-422 ◽  
Author(s):  
Matthew A. Beauregard ◽  
Qin Sheng
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Finite Difference ◽  
Nonlinear Partial Differential Equation ◽  
Partial Differential ◽  
Spatial Adaptation ◽  
Monitor Function ◽  
Monitoring Strategies ◽  
Highly Nonlinear ◽  
Equidistribution Principle

AbstractFinite difference computations that involve spatial adaptation commonly employ an equidistribution principle. In these cases, a new mesh is constructed such that a given monitor function is equidistributed in some sense. Typical choices of the monitor function involve the solution or one of its many derivatives. This straightforward concept has proven to be extremely effective and practical. However, selections of core monitoring functions are often challenging and crucial to the computational success. This paper concerns six different designs of the monitoring function that targets a highly nonlinear partial differential equation that exhibits both quenching-type and degeneracy singularities. While the first four monitoring strategies are within the so-calledprimitiveregime, the rest belong to a later category of themodifiedtype, which requires the priori knowledge of certain important quenching solution characteristics. Simulated examples are given to illustrate our study and conclusions.

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