A new three-field formulation of the biharmonic problem and its finite element discretization

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• 作者：Lothar Banz ; Bishnu P. Lamichhane and Ernst P. Stephan
• 刊名：Numerical Methods for Partial Differential Equations
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：33
• 期：1
• 页码：199-217
• 全文大小：1683K
• ISSN：1098-2426

文摘

We consider a new three-field formulation of the biharmonic problem. The solution, the gradient and the Lagrange multiplier are the three unknowns in the formulation. Adding a stabilization term in the discrete setting we can use the standard Lagrange finite element to discretize the solution, whereas we use the Raviart-Thomas finite element to discretize the gradient. The Lagrange multipliers are constructed to achieve the optimal error estimate. Numerical results are presented to demonstrate the performance of our approach.