SOME A PRIORI ERROR ESTIMATES FOR FINITE ELEMENT APPROXIMATIONS OF ELLIPTIC AND PARABOLIC LINEAR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS

2014 ◽  
Vol 4 (5) ◽  
pp. 423-454 ◽  
Author(s):  
Christophe Audouze ◽  
Prasanth Nair
Keyword(s):  
Finite Element ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Error Estimates ◽  
Stochastic Partial Differential Equations ◽  
A Priori ◽  
A Priori Error Estimates ◽  
Partial Differential ◽  
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.

Sign in / Sign up

Export Citation Format

Share Document