Year: 2018
Numerical Mathematics: Theory, Methods and Applications, Vol. 11 (2018), Iss. 3 : pp. 655–672
Abstract
This paper is concerned with numerical approximation of elliptic interface problems via week Galerkin (WG) finite element method. This method allows the usage of totally discontinuous functions in approximation space and preserves the energy conservation law. In the implementation, the weak partial derivatives and the weak functions are approximated by polynomials with various degrees of freedom. The accuracy and the computational complexity of the corresponding WG scheme are significantly impacted by the selection of such polynomials. This paper presents an optimal combination for the polynomial spaces that minimizes the number of unknowns in the numerical scheme without compromising the accuracy of the numerical approximation. Moreover, the new WG algorithm allows the use of finite element partitions consisting of general polytopal meshes and can be easily generalized to high orders. Optimal order error estimates in both $H^1$ and $L^2$ norms are established for the present WG finite element solutions.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.2017-OA-0078
Numerical Mathematics: Theory, Methods and Applications, Vol. 11 (2018), Iss. 3 : pp. 655–672
Published online: 2018-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
-
A least-squares-based weak Galerkin finite element method for elliptic interface problems
Deka, Bhupen | Roy, PapriProceedings - Mathematical Sciences, Vol. 129 (2019), Iss. 5
https://doi.org/10.1007/s12044-019-0518-4 [Citations: 0] -
Numerical solutions for Biharmonic interface problems via weak Galerkin finite element methods
Kumar, Raman
Applied Mathematics and Computation, Vol. 467 (2024), Iss. P.128496
https://doi.org/10.1016/j.amc.2023.128496 [Citations: 0] -
Analysis and computation of a weak Galerkin scheme for solving the 2D/3D stationary Stokes interface problems with high-order elements
Kumar, Raman | Deka, BhupenJournal of Numerical Mathematics, Vol. 32 (2024), Iss. 4 P.347
https://doi.org/10.1515/jnma-2023-0112 [Citations: 0] -
A weak Galerkin finite-element method for singularly perturbed convection–diffusion–reaction problems with interface
Ahmed, Tazuddin | Baruah, Rashmita | Kumar, RamanComputational and Applied Mathematics, Vol. 42 (2023), Iss. 7
https://doi.org/10.1007/s40314-023-02438-z [Citations: 0] -
Optimal A Priori Error Estimates for Elliptic Interface Problems: Weak Galerkin Mixed Finite Element Approximations
Kumar, Raman | Deka, BhupenJournal of Scientific Computing, Vol. 97 (2023), Iss. 2
https://doi.org/10.1007/s10915-023-02333-z [Citations: 0] -
On the superconvergence of a WG method for the elliptic problem with variable coefficients
Wang, Junping | Wang, Xiaoshen | Ye, Xiu | Zhang, Shangyou | Zhu, PengScience China Mathematics, Vol. 67 (2024), Iss. 8 P.1899
https://doi.org/10.1007/s11425-022-2097-8 [Citations: 0] -
Weak Galerkin finite element methods for electric interface model with nonhomogeneous jump conditions
Deka, Bhupen | Roy, PapriNumerical Methods for Partial Differential Equations, Vol. 36 (2020), Iss. 4 P.734
https://doi.org/10.1002/num.22446 [Citations: 8] -
Weak Galerkin Finite Element Methods for Parabolic Interface Problems with Nonhomogeneous Jump Conditions
Deka, Bhupen | Roy, PapriNumerical Functional Analysis and Optimization, Vol. 40 (2019), Iss. 3 P.259
https://doi.org/10.1080/01630563.2018.1549074 [Citations: 17] -
High-order weak Galerkin scheme for H(div)-elliptic interface problems
Kumar, Raman | Deka, BhupenJournal of Computational and Applied Mathematics, Vol. 432 (2023), Iss. P.115269
https://doi.org/10.1016/j.cam.2023.115269 [Citations: 2] -
WEAK GALERKIN FINITE ELEMENT METHODS COMBINED WITH CRANK-NICOLSON SCHEME FOR PARABOLIC INTERFACE PROBLEMS
Deka, Bhupen | Roy, Papri | Kumar, NareshJournal of Applied Analysis & Computation, Vol. 10 (2020), Iss. 4 P.1433
https://doi.org/10.11948/20190218 [Citations: 1]