Weak convergence for a stochastic exponential integrator and finite element discretization of stochastic partial differential equation with multiplicative & additive noise

2016 ◽  
Vol 108 ◽  
pp. 57-86 ◽  
Author(s):  
Antoine Tambue ◽  
Jean Medard T. Ngnotchouye
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Finite Element ◽  
Weak Convergence ◽  
Additive Noise ◽  
Stochastic Partial Differential Equation ◽  
Finite Element Discretization ◽  
Partial Differential ◽  
Element Discretization ◽  
Exponential Integrator

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.

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