
Optimal error estimate of the finite element approximation of second order semilinear nonautonomous parabolic PDEs
In this work, we investigate the numerical approximation of the second o...
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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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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 li...
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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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MDFEM: Multivariate decomposition finite element methods for elliptic PDEs with lognormal diffusion coefficients using higherorder QMC and FEM
We introduce the novel multivariate decomposition finite element method ...
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A hybrid MGAMSGD ANN training approach for approximate solution of linear elliptic PDEs
We introduce a hybrid "Modified Genetic AlgorithmMultilevel Stochastic ...
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A Practical Phase Field Method for an Elliptic Surface PDE
We consider a diffuse interface approach for solving an elliptic PDE on ...
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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 nonstandard finite element method for approximating H^2 strong solutions of second order linear elliptic PDEs in nondivergence form with continuous coefficients. To circumvent the difficulty of lacking an effective duality argument for this class of PDEs, a new analysis technique is introduced; the crux of it is to establish an H^1norm stability estimate for the finite element approximation operator which mimics a similar estimate for the underlying PDE operator recently established by the authors and its proof is based on a freezing coefficient technique and a topological argument. Moreover, both the H^1norm stability and error estimate also hold for the linear finite element method.
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