Ewing, Richard E.; Li, Zhilin; Lin, Tao; Lin, Yanping The immersed finite volume element methods for the elliptic interface problems. (English) Zbl 1027.65155 Math. Comput. Simul. 50, No. 1-4, 63-76 (1999). Summary: An immersed finite element space is used to solve the elliptic interface problems by a finite volume element method. Special nodal basis functions are introduced in a triangle whose interior intersects with the interface so that the jump conditions across the interface are satisfied. Optimal error estimates in an energy norm are obtained. Numerical results are supplied to justify the theoretical work and to reveal some interesting features of the method. Cited in 1 ReviewCited in 63 Documents MSC: 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 35J25 Boundary value problems for second-order elliptic equations 65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs 65N15 Error bounds for boundary value problems involving PDEs Keywords:immersed finite volume element methods; elliptic interface problems; convergence; error estimate; numerical results PDFBibTeX XMLCite \textit{R. E. Ewing} et al., Math. Comput. Simul. 50, No. 1--4, 63--76 (1999; Zbl 1027.65155) Full Text: DOI References: [1] Cai, Z., On the finite volume element method, Numer. Math., 58, 713-735 (1991) · Zbl 0731.65093 [2] R.E. Ewing, R.D. Lazarov, Y. Lin, Finite volume element approximations of non-local in time one-dimensional reactive flows in porous media, Computing. In press; R.E. Ewing, R.D. Lazarov, Y. Lin, Finite volume element approximations of non-local in time one-dimensional reactive flows in porous media, Computing. In press · Zbl 0969.76052 [3] R.E. Ewing, R.D. Lazarov, Y. Lin, Finite volume element approximations of nonlocal reactive transport flows in porous media, Technical Report ISC-98-07-MATH; R.E. Ewing, R.D. Lazarov, Y. Lin, Finite volume element approximations of nonlocal reactive transport flows in porous media, Technical Report ISC-98-07-MATH · Zbl 0961.76050 [4] Leveque, R. J.; Li, Z., The immersed interface for elliptic equations with discontinuous coefficients and singular sources, SIAM J. Numer. Anal., 31, 1019-1044 (1994) · Zbl 0811.65083 [5] Li, Z., The immersed interface method using a finite element formulation, Appl. Numer. Math., 27, 253-267 (1998) · Zbl 0936.65091 [6] Li, Z., Immersed interface methods for moving interface problems, Numer. Algorithms, 14, 269-293 (1997) · Zbl 0886.65096 [7] Li, Z., A fast iterative algorithm for elliptic interface problems, SIAM J. Numer. Anal., 35, 230-254 (1998) · Zbl 0915.65121 [8] R.H. Li, Z.Y. Chen, The Generalized Difference Method for Differential Equations, Jilin University Publishing House, 1994; R.H. Li, Z.Y. Chen, The Generalized Difference Method for Differential Equations, Jilin University Publishing House, 1994 [9] Z. Li, T. Lin, Y. Lin, The immersed finite element approximations for elliptic and parabolic interface problems, Submitted for publication; Z. Li, T. Lin, Y. Lin, The immersed finite element approximations for elliptic and parabolic interface problems, Submitted for publication [10] I.D. Mishev, Finite volume and finite volume element methods for non-symmetric problems, Ph.D. Thesis, Texas A&M University, Technical Report ISC-96-04-MATH, 1997; I.D. Mishev, Finite volume and finite volume element methods for non-symmetric problems, Ph.D. Thesis, Texas A&M University, Technical Report ISC-96-04-MATH, 1997 [11] Mishev, I. D., Finite volume methods on Voronoi Meshes, Numerical Methods for Partial Differential Equations, 14, 193-212 (1998) · Zbl 0903.65083 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.