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Title: | Hdg method for nonlinear parabolic integro-differential equations |
Authors: | Yadav, Sangita |
Keywords: | Mathematics Hybridizable discontinuous galerkin (HDG) Integro-differential equations Lipschitz continuit Super-convergence |
Issue Date: | Apr-2024 |
Publisher: | De Gruyter |
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(hk+1) when polynomials of degree k≥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. |
URI: | https://www.degruyter.com/document/doi/10.1515/cmam-2023-0060/html http://dspace.bits-pilani.ac.in:8080/jspui/handle/123456789/17637 |
Appears in Collections: | Department of Mathematics |
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