Higher-order NIPG methods on Bakhvalov-type meshes for a singularly perturbed Volterra integro-differential equation

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Abstract

In the present article, a higher-order NIPG method on a Bakhvalov-type mesh is developed to solve a second-order singularly perturbed Volterra integro-differential equation. Drawing on the distinctive properties of Bakhvalov-type meshes, we construct a composite interpolation operator, which enables the derivation of parameter-uniform error estimates for the proposed NIPG method. It is shown that the accuracy of this method attains an order of k in the energy norm, where k denotes the degree of the piecewise polynomials employed in the finite element space. Numerical experiments are presented to confirm our theoretical results.

Keywords

singularly perturbed / Volterra integro-differential equation / NIPG method / Bakhvalov-type mesh / uniform convergence

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