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A priori hp-estimates for discontinuous Galerkin approximations to linear hyperbolic integro-differential equations

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Title A priori hp-estimates for discontinuous Galerkin approximations to linear hyperbolic integro-differential equations
 
Creator KARAA, S
PANI, AK
YADAV, S
 
Subject FINITE-ELEMENT METHODS
WAVE-EQUATION
DIFFERENTIAL-EQUATIONS
DIFFUSION-PROBLEMS
ELLIPTIC PROBLEMS
CONVECTION
QUADRATURE
Local discontinuous Galerkin method
Linear second order hyperbolic integro-differential equation
Nonstandard formulation
Semidiscrete and completely discrete schemes
Mixed type Ritz-Volterra projection
Role of stabilizing parameters
hp-Error estimates
Order of convergence
Numerical experiments
 
Description An hp-discontinuous Galerkin (DG) method is applied to a class of second order linear hyperbolic integro-differential equations. Based on the analysis of an expanded mixed type Ritz-Volterra projection, a priori hp-error estimates in L-infinity (L-2)-norm of the velocity as well as of the displacement, which are optimal in the discretizing parameter h and suboptimal in the degree of polynomial p are derived. For optimal estimates of the displacement in L-infinity(L-2)-norm with reduced regularity on the exact solution, a variant of Baker's nonstandard energy formulation is developed and analyzed. Results on order of convergence which are similar in spirit to linear elliptic and parabolic problems are established for the semidiscrete case after suitably modifying the numerical fluxes. For the completely discrete scheme, an implicit-in-time procedure is formulated, stability results are derived and a priori error estimates are discussed. Finally, numerical experiments on two dimensional domains are conducted which confirm the theoretical results. (C) 2015 IMACS. Published by Elsevier B.V. All rights reserved.
 
Publisher ELSEVIER SCIENCE BV
 
Date 2016-01-14T12:54:40Z
2016-01-14T12:54:40Z
2015
 
Type Article
 
Identifier APPLIED NUMERICAL MATHEMATICS, 96,1-23
0168-9274
1873-5460
http://dx.doi.org/10.1016/j.apnum.2015.04.006
http://dspace.library.iitb.ac.in/jspui/handle/100/17549
 
Language en