Affiliation:
1. Department of Mathematics , 29794 Birla Institute of Technology and Science , Pilani , Pilani Campus, Pilani Rajasthan , India
Abstract
Abstract
The hybridizable discontinuous Galerkin (HDG) method has been applied to a nonlinear parabolic integro-differential equation.
The nonlinear functions are considered to be Lipschitz continuous to analyze uniform in time a priori bounds.
An extended type Ritz–Volterra projection is introduced and used along with the HDG projection as an intermediate projection to achieve optimal order convergence of
O
(
h
k
+
1
)
O(h^{k+1})
when polynomials of degree
k
≥
0
k\geq 0
are used to approximate both the solution and the flux variables.
By relaxing the assumptions in the nonlinear variable, super-convergence is achieved by element-by-element post-processing.
Using the backward Euler method in temporal direction and quadrature rule to discretize the integral term, a fully discrete scheme is derived along with its error estimates.
Finally, with the help of numerical examples in two-dimensional domains, computational results are obtained, which verify our results.
Funder
Department of Science and Technology, Ministry of Science and Technology, India