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Error Estimates and Superconvergence of RT0Mixed Methods for a Class of semilinear elliptic Optimal Control Problems

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Numerical Mathematics(Theory,Methods and Applications) 2013年第4期6卷 637-656页

作者： Yanping Chen Tianliang Hou School of Mathematical Sciences South China Normal UniversityGuangzhou 510631GuangdongChina Research Institute of Hong Kong Baptist University in Shenzhen Shenzhen 518057GuangdongChina

In this paper,we will investigate the error estimates and the superconvergence property of mixed finite element methods for a semilinear elliptic control problem with an integral constraint on *** state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element and the control variable is approximated by piecewise constant *** derive some superconvergence properties for the control variable and the state ***,we derive L∞-and H−1-error estimates both for the control variable and the state ***,a numerical example is given to demonstrate the theoretical results.

关键词： semilinear elliptic equations optimal control problems superconvergence error estimates mixed finite element methods

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Superconvergence and L^(∞)-Error Estimates of RT1Mixed Methods for semilinear elliptic Control Problems with an Integral Constraint

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Numerical Mathematics(Theory,Methods and Applications) 2012年第3期5卷 423-446页

作者： Yanping Chen Tianliang Hou School of Mathematical Sciences South China Normal UniversityGuangzhou 510631GuangdongChina Hunan Key Laboratory for Computation and Simulation in Science and Engineering Department of MathematicsXiangtan UniversityXiangtan 411105HunanChina

In this paper,we investigate the superconvergence property and the L∞-error estimates of mixed finite element methods for a semilinear elliptic control problem with an integral *** state and co-state are approximated by the order one Raviart-Thomas mixed finite element space and the control variable is approximated by piecewise constant functions or piecewise linear *** derive some superconvergence results for the control variable and the state variables when the control is approximated by piecewise constant ***,we derive L∞-error estimates for both the control variable and the state variables when the control is discretized by piecewise linear ***,some numerical examples are given to demonstrate the theoretical results.

关键词： semilinear elliptic equations optimal control problems superconvergence L∞-error estimates mixed finite element methods postprocessing

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Higher Order Estimates for Boundary Blow-Up Solutions of elliptic equations with Gradient Term

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Journal of Mathematical Research with Applications 2021年第2期41卷 161-170页

作者： Yajie ZHANG Feiyao MA Weifeng WO Department of Mathematics Ningbo University

In this paper,the higher order asymptotic behaviors of boundary blow-up solutions to the equation■ in bounded smooth domain■ are systematically investigated for p and *** second and third order boundary behaviours of the equation are *** results show the role of the mean curvature of the boundary■ and its gradient in the high order asymptotic expansions of the solutions.

关键词： second order estimates third order estimates semilinear elliptic equations

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Ground State Solutions for a semilinear elliptic Equation Involving Concave-Convex Nonlinearities

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Journal of Partial Differential equations 2013年第1期26卷 14-24页

作者： KHAZAEE KOHPAR O. KHADEMLOO S. Department of Basic Sciences Babol University of Technology 47148-71167Babol Iran.

This work is devoted to the existence and multiplicity properties of the ground state solutions of the semilinear boundary value problem - Au = Aa （x） u I u Iq- 2 ＋ b（x）u｜u｜2.-2 in a bounded domain coupled with Dirichlet boundary condition. Here 2＊ is the critical Sobolev exponent, and the term ground state refers to minimizers of the corresponding energy within the set of nontrivial positive solutions. Using the Ne- hari manifold method we prove that one can find an interval A such that there exist at least two positive solutions of the problem for A E A.

关键词： semilinear elliptic equations Nehari manifold concave-convex nonlinearities.

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