A New Family of High Regularity Elements

作者：Sun Jiguang^*

来源：Numerical Methods for Partial Differential Equations, 2012, 28(1): 1-16.

DOI：10.1002/num.20601

• biharmonic equation
• high regularity finite element
• partition of unity

In this article, we propose a new family of high regularity finite element spaces. The global approximation spaces are obtained in two steps. We first build an open cover of the computational domain and local approximation spaces on each patch of the cover. Then we construct partition of unity functions subordinate to the open cover depending on the regularity requirement. The basis functions of the global space is given by the products of the local basis functions and the corresponding partition of unity functions. The method can be used to construct finite element spaces of any desired regularity. Approximation properties and implementation details are discussed. Numerical examples for the biharmonic equation are presented to show the effectiveness of the proposed method.

• 出版日期2012-1