A priori error estimates for finite element approximations of parabolic stochastic partial differential equations with generalized random variables

Stochastics ◽  
2015 ◽  
Vol 87 (4) ◽  
pp. 537-561
Author(s):  
Christophe Audouze ◽  
Prasanth B. Nair
Keyword(s):  
Finite Element ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Error Estimates ◽  
Stochastic Partial Differential Equations ◽  
A Priori ◽  
Random Variables ◽  
A Priori Error Estimates ◽  
Finite Element Approximations ◽  
Priori Error Estimates

scholarly journals A New Mixed Element Method for a Class of Time-Fractional Partial Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Yang Liu ◽  
Hong Li ◽  
Wei Gao ◽  
Siriguleng He ◽  
Zhichao Fang
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Error Estimates ◽  
A Priori ◽  
A Priori Error Estimates ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Priori Error Estimates ◽  
Mixed Element ◽  
Element Method

A kind of new mixed element method for time-fractional partial differential equations is studied. The Caputo-fractional derivative of time direction is approximated by two-step difference method and the spatial direction is discretized by a new mixed element method, whose gradient belongs to the simpleL2Ω2space replacing the complexH(div;Ω)space. Some a priori error estimates inL2-norm for the scalar unknownuand inL22-norm for its gradientσ. Moreover, we also discuss a priori error estimates inH1-norm for the scalar unknownu.

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