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

Samir Karaa, Amiya K. Pani*, Sangita Yadav

*المؤلف المقابل لهذا العمل

نتاج البحث: المساهمة في مجلةمراجعة النظراء

2 اقتباسات (Scopus)

ملخص

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∞(L2)-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∞(L2)-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.

اللغة الأصليةEnglish
الصفحات (من إلى)1-23
عدد الصفحات23
دوريةApplied Numerical Mathematics
مستوى الصوت96
المعرِّفات الرقمية للأشياء
حالة النشرPublished - مايو 6 2015

ASJC Scopus subject areas

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