一种扭曲网格下扩散方程的有限元修补技术

A Finite Element Repair Technique for Diffusion Equations on Distorted Meshes

针对扭曲网格上的扩散方程,笔者提出了一种有限元全局修补技术,并证明了修补后的有限元解不仅满足离散的极值原理,而且保持全局能量守恒。数值实验结果表明:当扩散系数强各向异性时,全局修补技术比已有的局部修补技术的计算开销更小。

On the basis of the diffusion equations on distorted meshes,a finite element global repair technique is proposed in this paper.It is proved that the repaired finite element solutions not only satisfy the discrete maximum principle but also keep the total energy conservation.Numerical experiments show that when diffusion tensors are strongly anisotropic,global repair technique has less computational cost than existing local repair technique.