Error estimates of the discretization of linear parabolic equations on general nonconforming spatial grids. (Des estimations d’erreurs pour la discrétisation des équations paraboliques sur une classe générale multidimensionnelle de maillages non conformes.) (English) Zbl 1201.65167

Bradji, Abdallah; Fuhrmann, Jürgen

C. R., Math., Acad. Sci. Paris 348, No. 19-20, 1119-1122 (2010).

Summary: A general class of nonconforming meshes was recently used to approximate stationary anisotropic heterogeneous diffusion problems in any space dimensions [R. Eymard, T. Gallouët and R. Herbin, IMA J. Numer. Anal. 30, No. 4, 1009–1043 (2010; Zbl 1202.65144)]. The aim of the present work is to deal with some error estimates of the discretization of parabolic equations on this general class of meshes in several space dimensions. We present an implicit scheme based on an orthogonal projection of the exact initial function. We provide error estimates in discrete norms \(\mathbb L^\infty (0, T; H^1_0(\Omega ))\) and \(\mathcal W^{1, \infty }(0, T; \mathbb L^2(\Omega ))\).

MSC:

65M15	Error bounds for initial value and initial-boundary value problems involving PDEs
65M50	Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
35K60	Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations

Citations:

Zbl 1202.65144

References:

[1]	Eymard, R.; Gallouët, T.; Herbin, R., Discretization of heterogeneous and anisotropic diffusion problems on general nonconforming meshes, IMA Journal of Numerical Analysis (2009), Advance Access published on June 16 · Zbl 1202.65144