scholarly journals A Priori $L_2 $ Error Estimates for Galerkin Approximations to Parabolic Partial Differential Equations

1973 ◽  
Vol 10 (4) ◽  
pp. 723-759 ◽  
Author(s):  
Mary Fanett Wheeler
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Error Estimates ◽  
A Priori ◽  
Parabolic Partial Differential Equations ◽  
Partial Differential ◽  
Galerkin Approximations

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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