
Adaptive FirstOrder System LeastSquares Finite Element Methods for Second Order Elliptic Equations in NonDivergence Form
This paper studies adaptive firstorder leastsquares finite element met...
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H^1norm error estimate for a nonstandard finite element approximation of secondorder linear elliptic PDEs in nondivergence form
This paper establishes the optimal H^1norm error estimate for a nonstan...
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Error estimation for secondorder PDEs in nonvariational form
Secondorder partial differential equations in nondivergence form are c...
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Uniform Höldernorm bounds for finite element approximations of secondorder elliptic equations
We develop a discrete counterpart of the De GiorgiNashMoser theory, wh...
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A Conservative Finite Element Solver for MHD Kinematics equations: Vector Potential method and Constraint Preconditioning
A new conservative finite element solver for the threedimensional stead...
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Mixed (LL^*)^1 and LL^* leastsquares finite element methods with application to linear hyperbolic problems
In this paper, a few dual leastsquares finite element methods and their...
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Hessian discretisation method for fourth order semilinear elliptic equations: applications to the von Kármán and Navier–Stokes models
This paper deals with the Hessian discretisation method (HDM) for fourth...
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C^0 finite element approximations of linear elliptic equations in nondivergence form and HamiltonJacobiBellman equations with Cordes coefficients
This paper is concerned with C^0 finite element approximations of the linear elliptic equations in nondivergence form and the HamiltonJacobiBellman (HJB) equations with Cordes coefficients. Motivated by the MirandaTalenti estimate, a discrete analog is proved once the finite element space is C^0 on the (n1)dimensional subsimplex (face) and C^1 on (n2)dimensional subsimplex. The main novelty of the nonstandard finite element methods is to introduce an interior penalty term to argument the PDEinduced variational form of the linear elliptic equations in nondivergence form or the HJB equations. As a distinctive feature of the proposed methods, no penalization or stabilization parameter is involved in the variational forms. As a consequence, the coercivity constant (resp. monotonicity constant) for the linear elliptic equations in nondivergence form (resp. the HJB equations) at discrete level is exactly the same as that from PDE theory. Numerical experiments are provided to validate the convergence theory and to illustrate the accuracy and computational efficiency of the proposed methods.
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