Anisotropic error analysis of weak Galerkin finite element method for singularly perturbed biharmonic problems
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| Názov: | Anisotropic error analysis of weak Galerkin finite element method for singularly perturbed biharmonic problems |
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| Autori: | Aayushman Raina, Srinivasan Natesan, Şuayip Toprakseven |
| Zdroj: | Mathematics and Computers in Simulation. 229:203-221 |
| Publication Status: | Preprint |
| Informácie o vydavateľovi: | Elsevier BV, 2025. |
| Rok vydania: | 2025 |
| Predmety: | anisotropic estimates, 65N30, 65N15, 35J30, Error bounds for boundary value problems involving PDEs, Shishkin mesh, Numerical Analysis (math.NA), Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Higher-order elliptic equations, 01 natural sciences, FOS: Mathematics, weak Galerkin finite element method, biharmonic problem, singular perturbation problem, Mathematics - Numerical Analysis, 0101 mathematics |
| Popis: | We consider the Weak Galerkin finite element approximation of the Singularly Perturbed Biharmonic elliptic problem on a unit square domain with clamped boundary conditions. Shishkin mesh is used for domain discretization as the solution exhibits boundary layers near the domain boundary. Error estimates in the equivalent $H^{2}-$ norm have been established and the uniform convergence of the proposed method has been proved. Numerical examples are presented corroborating our theoretical findings. |
| Druh dokumentu: | Article |
| Popis súboru: | application/xml |
| Jazyk: | English |
| ISSN: | 0378-4754 |
| DOI: | 10.1016/j.matcom.2024.09.017 |
| DOI: | 10.48550/arxiv.2409.07217 |
| Prístupová URL adresa: | http://arxiv.org/abs/2409.07217 https://zbmath.org/8031533 https://doi.org/10.1016/j.matcom.2024.09.017 |
| Rights: | Elsevier TDM CC BY NC ND |
| Prístupové číslo: | edsair.doi.dedup.....98a333bfa5e5051d2a1a208fde3ae32b |
| Databáza: | OpenAIRE |
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Nájsť tento článok vo Web of Science | Abstrakt: | We consider the Weak Galerkin finite element approximation of the Singularly Perturbed Biharmonic elliptic problem on a unit square domain with clamped boundary conditions. Shishkin mesh is used for domain discretization as the solution exhibits boundary layers near the domain boundary. Error estimates in the equivalent $H^{2}-$ norm have been established and the uniform convergence of the proposed method has been proved. Numerical examples are presented corroborating our theoretical findings. |
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| ISSN: | 03784754 |
| DOI: | 10.1016/j.matcom.2024.09.017 |