Mimetic finite difference approximation of quasilinear elliptic problems

被引：11

作者：

Antonietti, Paola F. ^{[1
]}

Bigoni, Nadia ^{[1
]}

Verani, Marco ^{[1
]}

机构：

[1] Politecn Milan, MOX, Dipartimento Matemat F Brioschi, I-20133 Milan, Italy

来源：

CALCOLO | 2015年 / 52卷 / 01期

关键词：

MFD method; Quasilinear elliptic problems; Kacanov method; POSTERIORI ERROR ESTIMATORS; VIRTUAL ELEMENT METHODS; POLYHEDRAL MESHES; NEWTONIAN FLOWS; STOKES PROBLEM; DIFFUSION-PROBLEMS; POLYGONAL MESHES; CONVERGENCE; DISCRETIZATION; EQUATIONS;

D O I：

10.1007/s10092-014-0107-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work we approximate the solution of a quasilinear elliptic problem of monotone type by using the Mimetic Finite Difference (MFD) method. Under a suitable approximation assumption, we prove that the MFD approximate solution converges, with optimal rate, to the exact solution in a mesh-dependent energy norm. The resulting nonlinear discrete problem is then solved iteratively via linearization by applying the Kaanov method. The convergence of the Kaanov algorithm in the discrete mimetic framework is also proved. Several numerical experiments confirm the theoretical analysis.

引用

页码：45 / 67

页数：23

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