Improvement of the Constructive A Priori Error Estimates for a Fully Discretized Periodic Solution of Heat Equation
-
Takuma Kimura
,
Teruya Minamoto
and
Mitsuhiro T. Nakao
Abstract
In this study, we present new sharper constructive a priori error estimates for a full-discrete numerical solution of the heat equation that refines our previous work. The full discretization is given using the finite element method in space and linear interpolation in time, similar to that in the previous work. In particular, we adopt an approach based on the effective use of the properties both for exact and discretized time-periodic solutions to establish the error estimates simpler and sharper than the previous work. Furthermore, we derive some time-stepwise error estimates in the space direction. Finally, we present several numerical examples that confirm the actual refinements of the convergence.
Funding source: Japan Society for the Promotion of Science
Award Identifier / Grant number: 17K17948
Award Identifier / Grant number: 18K03434
Award Identifier / Grant number: 20K03752
Funding statement: This work was partially supported by JSPS KAKENHI Grant Number 17K17948, 18K03434 and 20K03752.
Acknowledgements
The authors are grateful to the two reviewers for their very helpful comments and suggestions.
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Articles in the same Issue
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Articles in the same Issue
- Frontmatter
- On the Spectrum of an Operator Associated with Least-Squares Finite Elements for Linear Elasticity
- Anisotropic Adaptive Finite Elements for an Elliptic Problem with Strongly Varying Diffusion Coefficient
- DPG Methods for a Fourth-Order div Problem
- Stable Implementation of Adaptive IGABEM in 2D in MATLAB
- Optimal Convergence of the Newton Iterative Crank–Nicolson Finite Element Method for the Nonlinear Schrödinger Equation
- Partially Discontinuous Nodal Finite Elements for 𝐻(curl) and 𝐻(div)
- Improvement of the Constructive A Priori Error Estimates for a Fully Discretized Periodic Solution of Heat Equation
- An 𝐿𝑝-DPG Method with Application to 2D Convection-Diffusion Problems
- An Improvement on a Class of Fixed Point Iterative Methods for Solving Absolute Value Equations
- Low-Regularity Integrator for the Davey–Stewartson System: Elliptic-Elliptic Case
- The Numerical Approximation to a Stochastic Age-Structured HIV/AIDS Model with Nonlinear Incidence Rates
- Qualitative Properties of Space-Dependent SIR Models with Constant Delay and Their Numerical Solutions
- A Staggered Discontinuous Galerkin Method for Quasi-Linear Second Order Elliptic Problems of Nonmonotone Type
