A Priori Truncation Error Estimates for Stieltjes Fractions

1981 ◽  
pp. 203-211 ◽  
Author(s):  
Wolfgang J. Thron
Keyword(s):  
Error Estimates ◽  
Truncation Error ◽  
A Priori

scholarly journals Regularization of backward time-fractional parabolic equations by Sobolev-type equations

2020 ◽  
Vol 28 (5) ◽  
pp. 659-676
Author(s):  
Dinh Nho Hào ◽  
Nguyen Van Duc ◽  
Nguyen Van Thang ◽  
Nguyen Trung Thành
Keyword(s):  
Error Estimates ◽  
Parabolic Equations ◽  
Regularization Parameter ◽  
A Priori ◽  
Sobolev Type ◽  
A Posteriori ◽  
Parameter Choice ◽  
Numerical Tests ◽  
Ill Posed ◽  
Parameter Choice Rules

AbstractThe problem of determining the initial condition from noisy final observations in time-fractional parabolic equations is considered. This problem is well known to be ill-posed, and it is regularized by backward Sobolev-type equations. Error estimates of Hölder type are obtained with a priori and a posteriori regularization parameter choice rules. The proposed regularization method results in a stable noniterative numerical scheme. The theoretical error estimates are confirmed by numerical tests for one- and two-dimensional equations.

scholarly journals A note on a priori error estimates for augmented mixed methods

2016 ◽  
Vol 57 ◽  
pp. 139-144
Author(s):  
Tomás P. Barrios ◽  
Edwin Behrens ◽  
Rommel Bustinza
Keyword(s):  
Mixed Methods ◽  
Error Estimates ◽  
A Priori ◽  
A Priori Error Estimates ◽  
Priori Error Estimates

scholarly journals A Priori and A Posteriori Error Estimates for a Crank Nicolson Type Scheme of an Elliptic Problem with Dynamical Boundary Conditions

2016 ◽  
Vol 8 (2) ◽  
pp. 1
Author(s):  
Rola Ali Ahmad ◽  
Toufic El Arwadi ◽  
Houssam Chrayteh ◽  
Jean-Marc Sac-Epee
Keyword(s):  
Error Estimates ◽  
A Priori ◽  
A Posteriori Error Estimates ◽  
Time Discretization ◽  
Posteriori Error ◽  
A Posteriori ◽  
A Posteriori Error ◽  
Dynamical Boundary Conditions ◽  
Error Indicators ◽  
Crank Nicolson

In this article we claim that we are going to give a priori and a posteriori error estimates for a Crank Nicolson type scheme. The problem is discretized by the finite elements in space. The main result of this paper consists in establishing two types of error indicators, the first one linked to the time discretization and the second one to the space discretization.

ERROR ESTIMATES FOR LINEAR PDEs SOLVED BY WAVELET BASED TAYLOR–GALERKIN SCHEMES

2009 ◽  
Vol 07 (02) ◽  
pp. 143-162 ◽  
Author(s):  
MANI MEHRA ◽  
B. V. RATHISH KUMAR
Keyword(s):  
Error Estimates ◽  
A Priori ◽  
A Posteriori Error Estimates ◽  
Equivalent Norm ◽  
Posteriori Error ◽  
Discrete Problem ◽  
Fully Discrete ◽  
Time Stepping ◽  
Priori Estimates ◽  
Space Error

In this paper, we develop a priori and a posteriori error estimates for wavelet-Taylor–Galerkin schemes introduced in Refs. 6 and 7 (particularly wavelet Taylor–Galerkin scheme based on Crank–Nicolson time stepping). We proceed in two steps. In the first step, we construct the priori estimates for the fully discrete problem. In the second step, we construct error indicators for posteriori estimates with respect to both time and space approximations in order to use adaptive time steps and wavelet adaptivity. The space error indicator is computed using the equivalent norm expressed in terms of wavelet coefficients.

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