A general mixed covolume framework for constructing conservative schemes for elliptic problems
A general mixed covolume framework for constructing conservative schemes for elliptic problems
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DOI：
10.1090/s0025-5718-99-01090-x
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发表时间：
1999-07
期刊：
影响因子：
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通讯作者：
S. Chou;P. Vassilevski
中科院分区：
文献类型：
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作者：
S. Chou;P. Vassilevski
我们提出了一个一般框架的有限体积或covolume计划开发的二阶椭圆问题的混合形式，即，写为一阶系统。我们将这些方案连接到标准的混合有限元方法，通过一个一对一的试验和测试空间之间的转移算子。在非对称的情况下（对流扩散方程），我们证明了用最低阶Raviart-Thomas空间或其在不连续分段常数空间中的映象来近似通量变量的半阶收敛速度。在对称情况下（扩散方程），对于状态变量（例如，浓度）和流量。包括数值实验。
We present a general framework for the finite volume or covolume schemes developed for second order elliptic problems in mixed form, i.e., written as first order systems. We connect these schemes to standard mixed finite element methods via a one-to-one transfer operator between trial and test spaces. In the nonsymmetric case (convection-diffusion equation) we show one-half order convergence rate for the flux variable which is approximated either by the lowest order Raviart-Thomas space or by its image in the space of discontinuous piecewise constants. In the symmetric case (diffusion equation) a first order convergence rate is obtained for both the state variable (e.g., concentration) and its flux. Numerical experiments are included.