This article develops the primal hybrid finite element method with Lagrange multipliers to approximate nonlinear parabolic initial-boundary value problems with gradient type non-linearity.A modified elliptic projectio...This article develops the primal hybrid finite element method with Lagrange multipliers to approximate nonlinear parabolic initial-boundary value problems with gradient type non-linearity.A modified elliptic projection is used to produce optimal order error estimates for the semi-discrete and backward Euler-based complete discrete schemes.In addition,error estimates in L^(∞)-norm are established which are optimal in nature.Superconvergence result of the gradient in L^(∞)-norm is discussed for the error between the primal hybrid solution and elliptic projection.As a bi-product,the proposed analysis provides optimal error analysis for non-conforming CR-elements.Finally,numerical tests are performed to validate the theoretical findings.展开更多
基金support provided by the DST-FIST program(Govt.of India)for setting up the computinglab facility called Center for Mathematical&Financial Computing(C-MFC)at the LNM Institute of Information Technology under the scheme"Fund for Improvement of Science and Technology"(FIST-No.SR/FST/MS-I/2018/24).
文摘This article develops the primal hybrid finite element method with Lagrange multipliers to approximate nonlinear parabolic initial-boundary value problems with gradient type non-linearity.A modified elliptic projection is used to produce optimal order error estimates for the semi-discrete and backward Euler-based complete discrete schemes.In addition,error estimates in L^(∞)-norm are established which are optimal in nature.Superconvergence result of the gradient in L^(∞)-norm is discussed for the error between the primal hybrid solution and elliptic projection.As a bi-product,the proposed analysis provides optimal error analysis for non-conforming CR-elements.Finally,numerical tests are performed to validate the theoretical findings.
