Adaptive finite element methods (AFEM) represent a pivotal advancement in numerical analysis by dynamically refining computational meshes to achieve greater solution accuracy. These methods are ...
We consider second order explicit and implicit two-step time-discrete schemes for wave-type equations. We derive optimal order a posteriori estimates controlling the ...
SIAM Journal on Numerical Analysis, Vol. 49, No. 1/2 (2011), pp. 845-868 (24 pages) We bound the difference between the solution to the continuous Rudin—Osher—Fatemi (ROF) image smoothing model and ...
The purpose of this research is to establish methodologies of designing error-free algorithms for solving various problems in computational engineering. Focus is on the development of efficient ...
Optical systems employ a rich array of physical effects which are described by well-understood equations. However, for all but the simplest devices these equations are typically too complex to permit ...
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