»ã±¨±êÌâ (Title)£ºThe h-p version continuous Petrov-Galerkin method for Volterra integro-differential equations (Volterra»ý·Ö΢·Ö·½³ÌµÄh-p½ÐøPetrov-Galerkin²½Öè)

»ã±¨ÈË (Speaker)£ºÒ×Àû¾ü ½ÌÊÚ£¨ÉϺ£Ê¦·¶´óѧ£©

»ã±¨¹¦·ò (Time)£º2022Äê9ÔÂ29ÈÕ(ÖÜËÄ) 15:30-17:00

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»ã±¨ÌáÒª£ºIn this talk, we consider an h-p version of the continuous Petrov-Galerkin time-stepping method for linear and nonlinear Volterra integro-differential equations with smooth and non-smooth kernels. We establish a priori error estimates in the L^2 -, H^1- and L^\infty-norm that are completely explicit with respect to the local discretization and regularity parameters. Moreover, we show that exponential rates of convergence can be achieved for solutions with start-up singularities by using geometrically time partitions and linearly increasing polynomial degrees. Numerical experiments are provided to illustrate the theoretical results. This presentation is based on joint works with Prof. Benqi Guo (University of Manitoba).