Abstract
Local discontinuous Galerkin method is considered for time-dependent singularly perturbed semilinear problems with boundary layer. The method is equipped with a general numerical flux including two kinds of independent parameters. By virtue of the weighted estimates and suitably designed global projections, we establish optimal -th error estimate in a local region at a distance of from domain boundary. Here k is the degree of piecewise polynomials in the discontinuous finite element space and h is the maximum mesh size. Both semi-discrete LDG method and fully discrete LDG method with a third-order explicit Runge–Kutta time-marching are considered. Numerical experiments support our theoretical results.
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 11801396
Award Identifier / Grant number: 11802193
Funding source: Natural Science Foundation of Jiangsu Province
Award Identifier / Grant number: BK20170374
Funding statement: The first and third author were funded by National Natural Science Foundation of China grant 11801396, National Science Foundation of Jiangsu Province grant BK20170374 and Natural Science Foundation of the Jiangsu Higher Education Institution of China grant 17KJB110016. The second author was funded by National Natural Science Foundation of China grant 11802193 and Natural Science Foundation of the Jiangsu Higher Education Institution of China grant 18KJB130005.
Acknowledgements
The authors gratefully acknowledge the editor and two anonymous referees for their time and invaluable suggestions, which improve the quality of the paper to a large extent.
References
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Articles in the same Issue
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- Block-Adaptive Cross Approximation of Discrete Integral Operators
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Articles in the same Issue
- Frontmatter
- A Differentiable Mapping of Mesh Cells Based on Finite Elements on Quadrilateral and Hexahedral Meshes
- Block-Adaptive Cross Approximation of Discrete Integral Operators
- Local Discontinuous Galerkin Method for Time-Dependent Singularly Perturbed Semilinear Reaction-Diffusion Problems
- Weighted Estimates of the Cayley Transform Method for Abstract Differential Equations
- Numerical Analysis of a Stable Finite Volume Scheme for a Generalized Thermistor Model
- Partial Relaxation of 𝐶0 Vertex Continuity of Stresses of Conforming Mixed Finite Elements for the Elasticity Problem
- Instance-Optimal Goal-Oriented Adaptivity
- A Semi-Uniform Multigrid Algorithm for Solving Elliptic Interface Problems
- A Priori Analysis of an Anisotropic Finite Element Method for Elliptic Equations in Polyhedral Domains
- Error Analysis of Nitsche’s and Discontinuous Galerkin Methods of a Reduced Landau–de Gennes Problem
- Fast Bilinear Algorithms for Symmetric Tensor Contractions
- Morley FEM for a Distributed Optimal Control Problem Governed by the von Kármán Equations