1,721,046 research outputs found
Gamma-convergence of discrete approximations to interfaces with prescribed mean curvature
No full text
An Efficient Linear Scheme to Approximate Parabolic Free Free Boundary Problems: Error Estimates and Implementation
No full textNochetto, R.; Verdi, C.. (1987). An Efficient Linear Scheme to Approximate Parabolic Free Free Boundary Problems: Error Estimates and Implementation. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/4538
Front-tracking and variational methods to approximate interfaces with prescribed mean curvature
No full textGamma-convergence of discrete approximations to interfaces with prescribed mean curvature
No full textNumerical minimization of geometrical type problems related to calculus of variations
No full textThe minimization of the functional G(v)=H(Sv)+∫∂Ω m·v-∫Ω k·v is related to various geometrical type problems in calculus of variations, such as the minimal partition of a set, the segmentation of images, and the search for sets with prescribed curvature. The functional G is first regularized and next discretized by means of piecewise linear finite elements with numerical quadratures, thus allowing its actual minimization on a computer. The discrete functionals converge to G in the sense of Γ-convergence, which implies the convergence of the discrete minima to a minimum of G. Various numerical experiments illustrate the behaviour of the numerical algorithm
A posteriori error estimates for variable time-step discretizations of nonlinear evolution equations
No full textWe study the backward Euler method with variable time-steps for abstract evolution equations in Hilbert spaces. Exploiting convexity of the underlying potential or the angle-bounded condition, thereby assuming no further regularity, we derive novel a posteriori estimates of the discretization error in terms of computable quantities related
to the amount of energy dissipation or monotonicity residual. These estimators solely depend on the discrete solution and data and impose no constraints between consecutive time-steps. We also prove that they converge to zero with an optimal rate with respect to the regularity of the solution. We apply the abstract results to a number of concrete strongly nonlinear problems of parabolic type with degenerate or singular character
Error control of nonlinear evolution equations
No full textWe derive novel a posteriori error estimates for backward Euler approximations of evo- lution inequalities in Hilbert spaces. The underlying nonlinear (multivalued) monotone operator is subdifferential, or more generally angle-bounded. The estimates depend solely on the discrete so- lution data, impose no constraints between consecutive time-steps, exhibit explicit stability factors, and are optimal with respect to both order and regularity
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