Composite finite element approximation for nonlinear parabolic problems in nonconvex polygonal domains. Issue 6 (24th July 2018)

• Record Type: Journal Article
• Authors: Pramanick, Tamal; Sinha, Rajen Kumar
• Is Part Of: Numerical methods for partial differential equations. Volume 34:Issue 6(2018)
• Page Start: 2316
• Page End: 2335
• Publication Date: 2018-07-24
• Subjects: composite finite elements -- error estimate -- fully discrete -- nonconvex domain -- nonlinear parabolic problems -- spatially semidiscrete; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22293
• Languages: English
• ISSNs: 0749-159X

Abstract

Abstract : We study a new class of finite elements so‐called composite finite elements (CFEs), introduced earlier by Hackbusch and Sauter, Numer. Math ., 1997; 75:447‐472, for the approximation of nonlinear parabolic equation in a nonconvex polygonal domain. A two‐scale CFE discretization is used for the space discretizations, where the coarse‐scale grid discretized the domain at an appropriate distance from the boundary and the fine‐scale grid is used to resolve the boundary. A continuous, piecewise linear CFE space is employed for the spatially semidiscrete finite element approximation and the temporal discretizations is based on modified linearized backward Euler scheme. We derive almost optimal‐order convergence in space and optimal order in time for the CFE method in the L ∞ ( L 2 ) norm. Numerical experiment is carried out for an L ‐shaped domain to illustrate our theoretical findings.