[PDF] Top 20 A Stable Mixed Finite Element Scheme for the Second Order Elliptic Problems

... The mixed finite element methods (MFEM) are widely used in the theoretical analysis and computations of many areas of science and ...convergence order, it becomes more and more popular in the ... See full document

... The second order of accuracy difference scheme generated by Crank-Nicholson difference scheme for approximately solving multipoint nonlocal boundary value problem is ...difference scheme ... See full document

... proposed finite element methods for solving elliptic and elasticity problems with interfaces using locally modified ...For elliptic problems with interfaces, the finite ... See full document

... bolic problems. When applied to these problems, standard finite element and fi- nite difference methods usually exhibit some combination of nonphysical oscil- lation and excessive numerical ... See full document

... fourth order quadratic parabolic optimal control problem is ...the order k Raviart-Thomas mixed finite element spaces, and the control is approximated by piecewise polynomials of order k ... See full document

... control problems, for the objective function containing a gradient of the state variable, we use mixed finite element methods to discretize the state equation, so that the scalar variable and its flux ... See full document

... (DG) finite element discretiza- tion for the hydrostatic ...and second-order accurate in space and ...advection scheme is ensured by using a strong stability-preserving time integration ... See full document

... and Scheme 1 for several values of ...1.6, Scheme 1 is more accurate than RBF-FD and ...interpolant stable. RBF-HFD yields better accuracy than Scheme 1 for the optimal value of ...of ... See full document

... Optimal control problems have been so widely met in all kinds of practical problems. Now we mention their application of the optimal control problems (1.1)-(1.4). Let us recall the static temperature ... See full document

... convergence order from the sample meshes ranging from 40 to 500 with 10 increment is ...a second-order accuracy. Figure 3.4 (b) shows the convergence order to be ... See full document

... How to cite this paper: Harris, A., Harris, S. and Rauls, D. (2016) Numerical Experi- ments Using MATLAB: Superconvergence of Nonconforming Finite Element Approxi- mation for Second-Order ... See full document

... the finite element method is a phenomenon in which the finite element approximation converges to the exact solution at a rate higher than the optimal order error ...conforming ... See full document

... a stable extrinsic extended finite element method (SXFEM) is proposed to solve the second order elliptic equation with discontinuous coefficients and ...the stable enrichment ... See full document

... quasi-linear elliptic and hyperbolic systems, we did not discuss fully discrete discontinuous Galerkin finite element approximations of quasi-linear hyperbolic ...finite element methods which may serve ... See full document

... instance, problems which lead to steep gradients or even discontinuities in the ...for problems posed on sur- faces, as in Sokolov et ...FEM scheme, the solution may exhibit spurious oscillatory ... See full document

... RBF-based discretisation methods have emerged as a new attractive solver for partial differential equations (PDEs). They have the capability to work well for problems defined on irregular domains. Very accurate ... See full document

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... defined on a body-fitted mesh for the domain that contains a interface [1]. Another approach that has drawn more attention recently is the so-called immersed FEM [16], [17], [25]. This method constructs a finite ... See full document

... of elliptic boundary value problems is a classical topic arising from a wide range of applications such as elasticity problems and nu- clear and petroleum engineering ...a finite number of ... See full document

... The paper is an extended version of the presentation for the International Conference on Computational Science ICCS 2012 [Calo et. al. 2011]. The structure of the paper is the following. In Section 2 entitled Automatic ... See full document