SIAM Journal on Numerical Analysis · 1997 · 65 citations · 13 references
Natural SciencesMathematicsComputational MechanicsComputational PhysicsDifferential EquationsGreen's FunctionsIntegral EquationsKernel MethodsNumerical AlgorithmsNumerical AnalysisPartial Differential EquationsDifferential Equation SolversFredholm Integral EquationsFredholm TheoryGreen's Functions For Partial Differential EquationsIntegral Equation KernelsParabolic Green's FunctionsParabolic Partial Differential EquationsRegularization Of Integral Equations
A method for approximating the solution of self-adjoint parabolic equations backwards in time is presented. The technique uses the Green's function of the parabolic equation to formulate the problem as a first-kind Fredholm integral equation, and then does a regularized least-squares solution of the resulting discrete system. Error estimates and examples are presented. Direct knowledge of the kernel of the differential operator is not required.
13
Solutions of Ill-Posed Problems.
John B. Bell, V. Y. Arsenin · Mathematics of Computation · 1978 · 8.2K citations
An analysis of the finite element method
Advances in Water Resources · 1980 · 3.5K citations
Computing, Computational Engineering, Mechanical Engineering +12