## The reproducing kernel particle method for two-dimensional unsteady heat conduction problems.(English)Zbl 1398.74065

Summary: The numerical solution to two-dimensional unsteady heat conduction problem is obtained using the reproducing kernel particle method (RKPM). A variational method is employed to furnish the discrete equations, and the essential boundary conditions are enforced by the penalty method. Convergence analysis and error estimation are discussed. Compared with the numerical methods based on mesh, the RKPM needs only the scattered nodes instead of meshing the domain of the problem. The effectiveness of the RKPM for two-dimensional unsteady heat conduction problems is examined by two numerical examples.

### MSC:

 74F05 Thermal effects in solid mechanics 74S30 Other numerical methods in solid mechanics (MSC2010) 80A20 Heat and mass transfer, heat flow (MSC2010)
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### References:

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