Name
Title | ||
|---|---|---|
Mixed Finite Element Approximations of Parabolic Integro-Differential Equations with Nonsmooth Initial Data |
Abstract | ||
|---|---|---|
We analyze the semidiscrete mixed finite element methods for parabolic integro-differential equations that arise in the modeling of nonlocal reactive flows in porous media. A priori $L^2$-error estimates for pressure and velocity are obtained with both smooth and nonsmooth initial data. More precisely, a mixed Ritz-Volterra projection, introduced earlier by Ewing et al. in [SIAM J. Numer. Anal., 40 (2002), pp. 1538-1560], is used to derive optimal $L^2$-error estimates for problems with initial data in $H^2\cap H_0^1$. In addition, for homogeneous equations we derive optimal $L^2$-error estimates for initial data just in $L^2$. Here, we use an elementary energy technique and duality argument. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1137/080740490 | SIAM J. Numerical Analysis |
Keywords | Field | DocType |
nonsmooth initial data,smooth and nonsmooth initial data.,error estimate,semidiscrete mixed finite element,mixed finite element approximations,siam j. numer,mixed nite element method,derive optimal,cap h_0,and duality argument. key words. parabolic integro-dieren tial equation,parabolic integro-differential equations,mixed ritz-volterra projection,semidiscrete,initial data,optimal error estimate,elementary energy technique,duality argument,integro differential equation,mixed finite element method,porous media | Differential equation,Mathematical optimization,Mathematical analysis,A priori and a posteriori,Optimal estimation,Finite element method,Duality (optimization),Numerical analysis,Mathematics,Parabola,Mixed finite element method | Journal |
Volume | Issue | ISSN |
47 | 5 | 0036-1429 |
Citations | PageRank | References |
6 | 0.73 | 0 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Rajen K. Sinha | 1 | 15 | 2.05 |
| Richard E. Ewing | 2 | 252 | 45.87 |
| Raytcho D. Lazarov | 3 | 456 | 82.23 |