Recent Advances in Finite Element Methods with Applications, 2nd Edition
A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E: Applied Mathematics".
Deadline for manuscript submissions: 30 September 2026 | Viewed by 372
Editors
2. University of Chinese Academy of Sciences, Beijing 100049, China
Interests: numerical analysis; finite element method; structure preservation; multilevel method
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Special Issue Information
Dear Colleagues,
The finite element method is an important tool used in applied sciences. In close association with computational mechanics, it has been increasingly applied across various fields such as engineering, material sciences, environmental sciences, medicine, biology, physics, and chemistry. The finite element method also motivates extensive research on mathematics, providing specific structures for the firm theoretical foundation.
This Special Issue, as a follow-up to the first edition, aims to collect recent advances in the construction, theoretical analysis, implementation, and application of finite element methods. We invite investigators to contribute high-quality original research articles as well as review articles on recent advances in the following methods:
- Finite element algorithms and mathematical theories for both classical and new model problems;
- Applications of the method for real-world problems, either on a specific problem or about the trend of a whole area, where finite element methods are used as research tools or as conceptual foundations;
- Developments and principles of finite element software packages and platforms, as well as new techniques for a mid-way step, such as mesh generation.
Particular interest will be given to investigations concerning finite element methods in the era of neural networks, including
- Finite element method as a neural network surrogate model;
- Models integrating physics-informed neural networks and the finite element method;
- Enhancing finite element methods with neural network models;
- Neural network-based multiscale modeling in finite element analysis;
- Coupling finite element methods and deep learning to solve high-dimensional problems, etc.
Potential topics include, but are not limited to, Navier–Stokes equations, magnetohydrodynamic equations, Boussinesq equations, Einstein equations, large deformation elasticity, computational biomechanics and biomathematics, medical engineering, mathematical theories of finite element methods, and the interplay of finite element methods and machine learning. The Special Issue is open to contributions on all forms of finite element methods and on advanced methodologies for their implementation.
Dr. Shuo Zhang
Dr. Shihua Gong
Guest Editors
Manuscript Submission Information
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Keywords
- finite element methods
- neural networks
- mixed finite element methods
- spectral element method
- discontinuous Galerkin methods
- grid methods
- meshfree methods
- Loubignac iteration
- virtual element method
- Hpk-FEM
- Navier–Stokes equations
- magnetohydrodynamic equations
- Boussinesq equations
- large deformation elasticity
- algorithms of FEM
- applications of FEM
- machine learning
- implementation techniques of FEM
- computational physics, chemistry and mechanics
- computational biomechanics and biomathematics
- material modeling
- computational applied sciences
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