References
- B. Nayroles, G. Touzot, and P. Villon, Generalizing the Finite Element Method: Diffuse Approximation and Diffuse Elements, Comput. Mech., vol. 10, pp. 307–318, 1992.
- T. Belytschko, Y. Y. Lu, and L. Gu, Element-Free Galerkin Methods, Int. J. Numer. Methods Eng., vol. 37, pp. 229–256, 1994.
- H. Xiang and X. Zhang, Variational Multiscale Element-Free Galerkin Method and Precise Time Step Integration Method for Convection-Diffusion Problems, Numer. Heat Transfer, Part A, vol. 67, pp. 210–223, 2015.
- X. Zhang and P. Zhang, Heterogeneous Heat Conduction Problems by an Improved Element-Free Galerkin Method, Numer. Heat Transfer, Part B, vol. 65, pp. 359–375, 2014.
- S. N. Atluri and T. Zhu, A New Meshless Local Petrov–Galerkin (MLPG) Approach, Comput. Mech., vol. 22, pp. 117–127, 1998.
- L. Gao, K. Liu, and Y. Liu, A Meshless Method for Stress-Wave Propagation in Anisotropic and Cracked Media, Int. J. Eng. Sci., vol. 45, pp. 601–616, 2007.
- E. Shivanian, Meshless Local Petrov–Galerkin (MLPG) Method for Three-Dimensional Nonlinear Wave Equations Via Moving Least Squares Approximation, Eng. Anal. Boundary Elem., vol. 50, pp 249–257, 2015.
- X. T. Pham, Two-Dimensional Rosenthal Moving Heat Source Analysis Using the Meshless Element Free Galerkin Method, Numer. Heat Transfer, Part A, vol. 63, pp. 807–823, 2013.
- H. Huang and F. Costanzo, On the Use of Space–Time Finite Elements in the Solution of Elasto-Dynamic Problems with Strain Discontinuities, Comput. Methods Appl. Mech. Eng., vol. 191, pp. 5315–5343, 2002.
- J. Chessa and T. Belytschko, A Local Space–Time Discontinuous Finite Element Method, Comput. Methods Appl. Mech. Eng., vol. 195, pp. 1325–1343, 2006.
- J. Réthoré, A. Gravouil, and A. Combescure, A Combined Space–Time Extended Finite Element Method, Int. J. Numer. Methods Eng., vol. 64, pp. 260–284, 2005.
- S. Wang, J. Goldak, J. Zhou, S. Tchernov, and D. Downey, Simulation on the Thermal Cycle of a Welding Process by Space–Time Convection–Diffusion Finite Element Analysis, Int. J. Thermal Sci., vol. 48, pp. 936–947, 2009.
- D. K. Khalmanova and F. Costanzo, A Space-Time Discontinuous Galerkin Finite Element Method for Fully Coupled Linear Thermo-Elasto-Dynamic Problems with Strain and Heat Flux Discontinuities, Comput. Methods Appl. Mech. Eng., vol. 197, pp. 1323–1342, 2008.
- A. Legay, A. Zilian, and C. Janssen, A Rheological Interface Model And Its Space-Time Finite Element Formulation For Fluid-Structure Interaction, Int. J. Numer. Methods Eng., vol. 86, pp. 667–687, 2011.
- A. Zilian and A. Legay, The Enriched Space-Time Finite Element Method (EST) for Simultaneous Solution of Fluid-Structure Interaction, Int. J. Numer. Methods Eng., vol. 75, pp. 305–334, 2008.
- Z. K. Seymena, H. Yücel, and B. Karasözen, Distributed Optimal Control of Time-Dependent Diffusion–Convection–Reaction Equations Using Space–Time Discretization, J. Comput. Appl. Math., vol. 261, pp 146–157, 2014.
- M. Dumbser, O. Zanotti, A. Hidalgo, and D. S. Balsara, ADER-WENO Finite Volume Schemes with Space–Time Adaptive Mesh Refinement, J. Comput. Phys., vol. 248, pp. 257–286, 2013.
- F. Collino, T. Fouquet, and P. Joly, Conservative Space-Time Mesh Refinement Methods for the FDTD Solution of a Maxwell’s Equations, J. Comput. Phys., vol. 211, pp. 9–35, 2006.
- V. Kostin, V. Lisitsa, G. Reshetova, and V. Tcheverda, Local Time–Space Mesh Refinement for Simulation of Elastic Wave Propagation in Multi-Scale Media, J. Comput. Phys., vol. 281, pp. 669–689, 2014.
- N. Netuzhylov and A. Zilian, Space-Time Meshfree Collocation Method: Methodology and Application to Initial-Boundary Value Problems, Int. J. Numer. Methods Eng., vol. 80, pp. 355–380, 2009.
- C.-A. Wang, H. Sadat, and J.-Y. Tan, Meshless Method for Solving Transient Radiative and Conductive Heat Transfer in Two-Dimensional Complex Geometries, Numer. Heat Transfer, Part B, vol. 65, pp. 518–536, 2014.
- T. Sophy, A. Da Silva, and A. Kribèche, A Space–Time Meshless Method that Removes Numerical Oscillations When Solving PDEs with High Discontinuities, Numer. Heat Transfer, Part B, vol. 62, pp. 50–70, 2012.
- T. Sophy, H. Sadat, and C. Prax, A Meshless Formulation for Three-Dimensional Laminar Natural Convection, Numer. Heat Transfer, Part B, vol. 41, pp. 433–445, 2002.
- K. Reuther, B. Sarler, and M. Rettenmayr, Solving Diffusion Problems on an Unstructured, Amorphous Grid by a Meshless Method, Int. J. Thermal Sci., vol. 55, pp. 16–22, 2012.
- J. Crank, The Mathematics of Diffusion, 2nd ed., reprint, Clarendon Press, Oxford, 1979.