Superconvergence in Finite - Element Methods
نویسنده
چکیده
My research focuses on applied aspects of the calculus of variations and partial differential equations, particularly nonlinear equations arising from physics and chemistry, and numerical analysis and scientific computing, particularly finite-element analysis and numerical methods for interface motion. I have worked on mathematical and numerical problems arising from materials science, such as those of martensitic microstructure and epitaxial growth of crystalline thin films, and from biochemistry and biophysics, such as those of molecular solvation, electrostatics, and biological pattern formation. In what follows, I summarize my research accomplishments and list my publications.
منابع مشابه
Superconvergence of immersed finite element methods for interface problems
In this article, we study superconvergence properties of immersed finite element methods for the one dimensional elliptic interface problem. Due to low global regularity of the solution, classical superconvergence phenomenon for finite element methods disappears unless the discontinuity of the coefficient is resolved by partition. We show that immersed finite element solutions inherit all desir...
متن کاملJ. KSIAM Vol.8, No.2, 23-38, 2004 SUPERCONVERGENCE OF FINITE ELEMENT METHODS FOR LINEAR QUASI-PARABOLIC INTEGRO-DIFFERENTIAL EQUATIONS
We consider finite element methods applied to a class of quasi parabolic integro-differential equations in R. Global strong superconvergence, which only requires that partitions are quasi-uniform, is investigated for the error between the approximate solution and the Sobolev-Volterra projection of the exact solution. Two order superconvergence results are demonstrated in W (Ω) and Lp(Ω), for 2 ...
متن کاملSuperconvergence of mixed finite element methods for optimal control problems
In this paper, we investigate the superconvergence property of the numerical solution of a quadratic convex optimal control problem by using rectangular mixed finite element methods. The state and co-state variables are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions. Some realistic regularity a...
متن کاملL1-error Estimates and Superconvergence in Maximum Norm of Mixed Finite Element Methods for Nonfickian Flows in Porous Media
متن کامل
Superconvergence for Control-Volume Mixed Finite Element Methods on Rectangular Grids
We consider control-volume mixed finite element methods for the approximation of second-order elliptic problems on rectangular grids. These methods associate control volumes (covolumes) with the vector variable as well as the scalar, obtaining local algebraic representation of the vector equation (e.g., Darcy’s law) as well as the scalar equation (e.g., conservation of mass). We establish O(h2)...
متن کاملA Superconvergent Finite Element Scheme for the Reissner-mindlin Plate by Projection Methods
The Reissner-Mindlin model is frequently used by engineers for plates and shells of small to moderate thickness. This model is well known for its “locking” phenomenon so that many numerical approximations behave poorly when the thickness parameter tends to zero. Following the formulation derived by Brezzi and Fortin, we construct a new finite element scheme for the Reissner-Mindlin model using ...
متن کامل