scholarly journals A continuous/discontinuous Galerkin method and a priori error estimates for the biharmonic problem on surfaces

2017 ◽  
Vol 86 (308) ◽  
pp. 2613-2649 ◽  
Author(s):  
Karl Larsson ◽  
Mats G. Larson
Keyword(s):  
Galerkin Method ◽  
Error Estimates ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
A Priori ◽  
A Priori Error Estimates ◽  
Biharmonic Problem ◽  
Priori Error Estimates

scholarly journals A priori error estimates of Adams-Bashforth discontinuous Galerkin Methods for scalar nonlinear conservation laws

2018 ◽  
Vol 26 (3) ◽  
pp. 151-172
Author(s):  
Charles Puelz ◽  
Béatrice Rivière
Keyword(s):  
Conservation Laws ◽  
Galerkin Method ◽  
Error Estimates ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
A Priori ◽  
A Priori Error Estimates ◽  
Nonlinear Conservation Laws ◽  
Priori Error Estimates ◽  
Forward Euler

Abstract In this paper we show theoretical convergence of a second-order Adams-Bashforth discontinuous Galerkin method for approximating smooth solutions to scalar nonlinear conservation laws with E-fluxes. A priori error estimates are also derived for a first-order forward Euler discontinuous Galerkin method. Rates are optimal in time and suboptimal in space; they are valid under a CFL condition.

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