Energy norm error estimates of a hybrid high-order method for the linear parabolic integro-differential equations on general meshes
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915940666441728 |
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| author | Mohapatra, Achyuta Ranjan Dutta |
| author_facet | Mohapatra, Achyuta Ranjan Dutta |
| contents | We are concerned in designing a suitable numerical scheme based on the equal-order hybrid high-order (HHO) method for the linear parabolic integro-differential equations. The spatial discretization is made using the equal-order HHO method and subsequently we perform the stability analysis of the corresponding semi-discrete scheme. The convergence results are presented in suitably defined Bochner norms for the semi-discrete problem. Then a second-order temporal discretization is implemented on the time domain using a Crank-Nicolson scheme where the memory term is approximated using a composite trapezoidal quadrature rule. The stability of the resultant complete discrete schemes are analyzed followed by derivation of the error estimates of order $\mathcal{O}(τ^{2}+h^{k+1})$, $k\ge 0$ is the degree of local polynomial approximation, in discrete $l^{2}(0,T;H^{1}(Ω))$ and $l^{\infty}(0,T;H^{1}(Ω))$ like norms. Numerical illustrations are performed on some polygonal meshes validating the theoretical estimates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_15147 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Energy norm error estimates of a hybrid high-order method for the linear parabolic integro-differential equations on general meshes Mohapatra, Achyuta Ranjan Dutta Numerical Analysis 65M60, 65N15 We are concerned in designing a suitable numerical scheme based on the equal-order hybrid high-order (HHO) method for the linear parabolic integro-differential equations. The spatial discretization is made using the equal-order HHO method and subsequently we perform the stability analysis of the corresponding semi-discrete scheme. The convergence results are presented in suitably defined Bochner norms for the semi-discrete problem. Then a second-order temporal discretization is implemented on the time domain using a Crank-Nicolson scheme where the memory term is approximated using a composite trapezoidal quadrature rule. The stability of the resultant complete discrete schemes are analyzed followed by derivation of the error estimates of order $\mathcal{O}(τ^{2}+h^{k+1})$, $k\ge 0$ is the degree of local polynomial approximation, in discrete $l^{2}(0,T;H^{1}(Ω))$ and $l^{\infty}(0,T;H^{1}(Ω))$ like norms. Numerical illustrations are performed on some polygonal meshes validating the theoretical estimates. |
| title | Energy norm error estimates of a hybrid high-order method for the linear parabolic integro-differential equations on general meshes |
| topic | Numerical Analysis 65M60, 65N15 |
| url | https://arxiv.org/abs/2604.15147 |