Finite Element Methods and Their Applications

Dear Colleagues,

The finite element method (FEM) is a mature tool used to obtain the numerical solution of partial differential equations (PDEs) used in multiple engineering fields and physics domains, such as computational electromagnetics, microwave tomographic imaging, geophysics, nanotechnology, stress analysis, fluid flow, heat transport, and the analysis of inhomogeneous materials. 

Although the FEM is an expensive tool from a computational point of view, the capabilities of computational resources have increased almost exponentially in the last few years, making the FEM a very good alternative for design and analysis purposes. This brings more insight in the current engineering problems, and leads to better designs before manufacturing a prototype. 

This Special Issue, entitled “Finite Element Methods and Their Applications”, intends to collect selected review works written by well-known researchers in the field, as well as the current developments in the application of the FEM to engineering designs and physical problems in engineering and science. 

Topics addressed in this Special Issue include, but are not limited to, the following: 

• The finite element method in engineering designs.
• The finite element method in the numerical simulation of physical problems.
• The development of new basis functions for the FEM, and comparison between different sets.
• The impact of the chosen mesh truncation technique.
• Adaptive refinement and error estimation with methods and impact of different parameters.
• Advantages of emerging and growing computing hardware and software infrastructure for the FEM.
• Unconventional approaches to reducing FEM computational and memory complexity.
• Uncertainty quantification using FEM.
• New FEM solvers for large and multiscale modeling.
• Hybridization with other numerical tools.
• Best practices for the FEM, including open-source projects, reproducibility and programs.
• Artificial intelligence applied to FEM, or using FEM-based data.
• Analysis of multi-physics problems with FEM. 

Dr. Adrian Amor-Martin
Dr. Luis E. García-Castillo
Guest Editors

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• finite element method
• computational electromagnetics
• high-performance computing
• 3D modelling
• multi-scale structures
• multi-physics problems
• artificial intelligence
• computational modelling