scholarly journals Adaptive space-time BEM for the heat equation

2022 ◽  
Vol 107 ◽  
pp. 117-131 ◽  
Author(s):  
Gregor Gantner ◽  
Raymond van Venetië
Keyword(s):  
Heat Equation ◽  
Space Time

A parallel space–time boundary element method for the heat equation

2019 ◽  
Vol 78 (9) ◽  
pp. 2852-2866 ◽  
Author(s):  
Stefan Dohr ◽  
Jan Zapletal ◽  
Günther Of ◽  
Michal Merta ◽  
Michal Kravčenko
Keyword(s):  
Boundary Element Method ◽  
Heat Equation ◽  
Boundary Element ◽  
Space Time ◽  
Time Boundary ◽  
Element Method

scholarly journals Spatial Moduli of Non-Differentiability for Linearized Kuramoto–Sivashinsky SPDEs and Their Gradient

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1251
Author(s):  
Wensheng Wang
Keyword(s):  
Heat Equation ◽  
White Noise ◽  
Fourth Order ◽  
Gaussian Processes ◽  
Three Dimensional ◽  
Space Time ◽  
Symmetry Analysis ◽  
Stochastic Heat Equation ◽  
Moduli Of Continuity

We investigate spatial moduli of non-differentiability for the fourth-order linearized Kuramoto–Sivashinsky (L-KS) SPDEs and their gradient, driven by the space-time white noise in one-to-three dimensional spaces. We use the underlying explicit kernels and symmetry analysis, yielding spatial moduli of non-differentiability for L-KS SPDEs and their gradient. This work builds on the recent works on delicate analysis of regularities of general Gaussian processes and stochastic heat equation driven by space-time white noise. Moreover, it builds on and complements Allouba and Xiao’s earlier works on spatial uniform and local moduli of continuity of L-KS SPDEs and their gradient.

scholarly journals Fully discrete finite element data assimilation method for the heat equation

2018 ◽  
Vol 52 (5) ◽  
pp. 2065-2082 ◽  
Author(s):  
Erik Burman ◽  
Jonathan Ish-Horowicz ◽  
Lauri Oksanen
Keyword(s):  
Finite Element ◽  
Initial Data ◽  
Heat Equation ◽  
Time Derivative ◽  
Classical Problem ◽  
Classical Case ◽  
Space Time ◽  
Optimal Error Estimates ◽  
Element Approximation ◽  
Element Discretization

We consider a finite element discretization for the reconstruction of the final state of the heat equation, when the initial data is unknown, but additional data is given in a sub domain in the space time. For the discretization in space we consider standard continuous affine finite element approximation, and the time derivative is discretized using a backward differentiation. We regularize the discrete system by adding a penalty on the H2-semi-norm of the initial data, scaled with the mesh-parameter. The analysis of the method uses techniques developed in E. Burman and L. Oksanen [Numer. Math. 139 (2018) 505–528], combining discrete stability of the numerical method with sharp Carleman estimates for the physical problem, to derive optimal error estimates for the approximate solution. For the natural space time energy norm, away from t = 0, the convergence is the same as for the classical problem with known initial data, but contrary to the classical case, we do not obtain faster convergence for the L2-norm at the final time.

scholarly journals Sharp space-time regularity of the solution to stochastic heat equation driven by fractional-colored noise

2020 ◽  
Vol 38 (4) ◽  
pp. 747-768
Author(s):  
Randall Herrell ◽  
Renming Song ◽  
Dongsheng Wu ◽  
Yimin Xiao
Keyword(s):  
Heat Equation ◽  
Colored Noise ◽  
Space Time ◽  
Stochastic Heat Equation
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