Higher order approximation of biharmonic problem using the WEB-Spline based mesh-free method
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Rajashekar Naraveni
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Sudhakar Chaudhary
Abstract
In this paper, we consider a biharmonic equation with Navier boundary conditions and we decoupled this fourth order biharmonic equation into a system of second order equations. In numerics, there is an advantage because of this decoupling, i.e., one can use C 0 finite elements to solve the decoupled system instead of C 1 finite elements. For solving this decoupled system of second order equations, we use the weighted extended b-spline (WEB-Spline) based mesh-free finite element method. The WEB-Spline method does not require any mesh generation and eliminates the difficult, time-consuming preprocessing step. Also, by the WEB-Spline method higher order approximations are possible with relatively low dimensional spaces. Numerical results based on the WEB-Spline method are compared with the usual finite element method in order to demonstrate the efficiency of the proposed method.
Funding source: University Grants Commission, India.
Award Identifier / Grant number: ID No. 421249
Acknowledgment
First author acknowledges the support of University Grants Commission, India, for their financial support through Senior Research Fellowship (ID No. 421249).
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Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: None declared.
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Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
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© 2021 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Original Research Articles
- Slippage phenomenon in hydromagnetic peristaltic rheology with hall current and viscous dissipation
- Dissipativity analysis of delayed stochastic generalized neural networks with Markovian jump parameters
- Numerical solutions for strain-softening surrounding rock under three-dimensional principal stress condition
- The exact Riemann solutions to an isentropic non-ideal dusty gas flow under a magnetic field
- Higher order approximation of biharmonic problem using the WEB-Spline based mesh-free method
- Solution of non-linear time fractional telegraph equation with source term using B-spline and Caputo derivative
- Nonlinear stability and numerical simulations for a reaction–diffusion system modelling Allee effect on predators
- Computational analysis of heat and mass transfer in a micropolar fluid flow through a porous medium between permeable channel walls
- 3D structure of single and multiple vortices in a flow under rotation
- Interaction solutions of a variable-coefficient Kadomtsev–Petviashvili equation with self-consistent sources
Artikel in diesem Heft
- Frontmatter
- Original Research Articles
- Slippage phenomenon in hydromagnetic peristaltic rheology with hall current and viscous dissipation
- Dissipativity analysis of delayed stochastic generalized neural networks with Markovian jump parameters
- Numerical solutions for strain-softening surrounding rock under three-dimensional principal stress condition
- The exact Riemann solutions to an isentropic non-ideal dusty gas flow under a magnetic field
- Higher order approximation of biharmonic problem using the WEB-Spline based mesh-free method
- Solution of non-linear time fractional telegraph equation with source term using B-spline and Caputo derivative
- Nonlinear stability and numerical simulations for a reaction–diffusion system modelling Allee effect on predators
- Computational analysis of heat and mass transfer in a micropolar fluid flow through a porous medium between permeable channel walls
- 3D structure of single and multiple vortices in a flow under rotation
- Interaction solutions of a variable-coefficient Kadomtsev–Petviashvili equation with self-consistent sources
