Name
Title | ||
|---|---|---|
On 3D DDFV Discretization of Gradient and Divergence Operators: Discrete Functional Analysis Tools and Applications to Degenerate Parabolic Problems. |
Abstract | ||
|---|---|---|
We present a detailed survey of discrete functional analysis tools (consistency results, Poincare and Sobolev embedding inequalities, discrete W 1; p compactness, discrete compactness in space and in time) for the so-called Discrete Duality Finite Volume (DDFV) schemes in three space dimensions. We concentrate mainly on the 3D CeVe-DDFV scheme presented in [IMA J. Numer. Anal., 32 (2012), pp. 1574-1603]. Some of our results are new, such as a general time-compactness result based upon the idea of Kruzhkov (1969); others generalize the ideas known for the 2D DDFV schemes or for traditional two-point-flux finite volume schemes. We illustrate the use of these tools by studying convergence of discretizations of nonlinear elliptic-parabolic problems of Leray-Lions kind, and provide numerical results for this example. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1515/cmam-2013-0011 | COMPUTATIONAL METHODS IN APPLIED MATHEMATICS |
Keywords | Field | DocType |
Finite Volume Approximation,Discrete Duality,3D CeVe-DDFV,Convergence,Consistency,Discrete Compactness,Kruzhkov Time Compactness Lemma,Discrete Sobolev Embeddings,Degenerate Parabolic Problems | Applied mathematics,Discretization,Embedding,Mathematical analysis,Sobolev space,Compact space,Duality (optimization),Operator (computer programming),Finite volume method,Mathematics,Parabola | Journal |
Volume | Issue | ISSN |
13 | 4 | 1609-4840 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Boris Andreianov | 1 | 27 | 5.70 |
| Mostafa Bendahmane | 2 | 35 | 9.38 |
| Florence Hubert | 3 | 44 | 5.50 |