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A variational analysis for the moving finite element method for gradient flows
By using the Onsager principle as an approximation tool, we give a novel...
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A variational framework for the strain-smoothed element method
Recently, the strain-smoothed element (SSE) method has been developed fo...
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A finite element scheme for an initial value problem
A new Hamilton principle of convolutional type, completely compatible wi...
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On the development of symmetry-preserving finite element schemes for ordinary differential equations
In this paper we introduce a procedure, based on the method of equivaria...
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Stabilized finite element method for incompressible solid dynamics using an updated Lagrangian formulation
This paper proposes a novel way to solve transient linear, and non-linea...
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Machine Learning and Finite Element Method for Physical Systems Modeling
Modeling of physical systems includes extensive use of software packages...
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A novel X-FEM based fast computational method for crack propagation
This study suggests a fast computational method for crack propagation, w...
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Extended framework of Hamilton's principle applied to Duffing oscillation
The paper begins with a novel variational formulation of Duffing equation using the extended framework of Hamilton's principle (EHP). This formulation properly accounts for initial conditions, and it recovers all the governing differential equations as its Euler-Lagrange equation. Thus, it provides elegant structure for the development of versatile temporal finite element methods. Herein, the simplest temporal finite element method is presented by adopting linear temporal shape functions. Numerical examples are included to verify and investigate performance of non-iterative algorithm in the developed method.
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